While I agree that higher rpms gives you more power (torque x rpm = hp, kinda sorta), when I'm tired I can't spin. Since I'm tired once a race gets, oh, like 20 minutes old, this means I have to do something other than spin like mad when I sprint.
Plus, if you're spinning like mad, you're relatively unstable (relative to 90-110 rpm). You're unable to adapt to an unexpected circumstance. For example, if I'm spinning at 200 rpm and I need to suddenly swerve to avoid a big crash, it's harder to do so than at 80 or 90 rpm. Or say someone really leans hard into me because they want me to move over. If I'm spinning at 200 rpm I'll be much less stable than at even 110-120 rpm.
Just to set down some numbers, I'm comfy spinning at 100-110 rpms consistently when using 170 cranks. My TTs and FTP tests tend to average about 110-112 rpms until I blow, then I drop to something like 70-80 rpms. On 175 cranks, take about 15-20 rpms off the numbers. I sprint at rpms anywhere from 70 to 120+, and I've won and lost sprints at all sorts of rpms. I don't think I won one at 70 rpms, but I did pass a bunch of people.
Therefore, although it's good to do various spin drills, and it's good to be comfy at higher rpms, it's not necessarily what you want to do in a race or group riding situation.
When you respond to an attack, you need to increase power. Like mentioned before, you can get power in two different ways. Like automobile engines, you can do it using higher torque (somewhat lower rpms) or lower torque (somewhat higher rpms).
I think that I'm a wheezing diesel compared to Doc, therefore I can't afford to spin up too much - if I do, I explode. Instead, I need to take advantage of my torque.
Ultimately you want max out power, not necessarily max out cadence. Yes, you need to max out power to spin a 53x12 at 125 rpm. But that's pretty serious speed. I don't have my handy dandy cadence gear spreadsheet in front of me but I think it's north of 40 mph. If that's what it takes to respond to a "non-racing" attack (group rides and training crits), you're training with some pretty fast riders.
What I find newer racers do (i.e. those that are fit but haven't been racing for many years, so don't have some of the cycling musculature built up yet) is spin more than necessary. They lack the ultimate torque to turn over the big gears, so they naturally compensate by spinning lower gears higher. It's like my low-torque winter car - I have to rev the heck out of it to get it going "fun", with the car responding, sort of, once I hit 3-4k rpm. My other car, a bit more "conditioned", can accelerate firmly from 1200 rpm (it has twice the torque at 1200 rpm as my other car does max).
However, as racers acclimate to the somewhat unnatural cycling motion, they tend to build up that missing power, developing stronger glutes, hamstrings, quads, lower back, etc. They also get better at using their upper body to counteract the pushing-down-with-more-than-body-weight downstrokes, so they can coordinate multiple downstrokes of immense power (relatively speaking).
As an illustration of this, ride no-handed on a trainer (or if you're skilled, rollers or the road - I'm not skilled enough to do this, at least the following part). Pedal as hard as you can, no handed. You'll lift yourself out of the saddle, even if it's just slightly. When you can anchor your body securely at high rpms against that "body float", you're doing well.
So, with the original situation - accelerate out of the saddle initially, then keep accelerating while sitting - this is what happens.
First, when you get out of the saddle, you increase your wind resistance. However, you can really anchor your body securely (because you're pulling on the bars), giving you a stable platform from which you can really put out a lot of lower-rpm torque. You accelerate until you start to max out your speed/cadence.
Then you sit, reducing your wind profile. You accelerate a bit simply from that, if you really have a lower wind profile. If you can keep accelerating, great. If not, you maintain speed. I think that it's very possible I'm more aero sprinting out of the saddle than I am sitting, since I'm close to my aero tuck while sprinting (way over the bars). I don't know definitively, but my point is that it's possible that sprinting in the saddle is not more aero than standing, esp for shorter people like me.
For me that "stage one" out of saddle acceleration is probably about 110-120 rpms max, and I like to jump (apparently, based on power data where ideal jump rpm = max instant power) from 90-100 rpm. Therefore I accelerate maybe 2 mph (8 or so rpm) to 5 mph (20 rpm) in one gear.
If I start to spin out, I stay standing and shift up again. A typical sprint is two shifts, unless I jump in a huge gear or very, very late (like 30-40 meters from the line due to being boxed in). Then it may be just one shift, or, in extreme cases, I jump in my biggest gear and therefore can't shift.
Note: I rarely contest downhill sprints since my only strength, my jump, is practically useless in such sprints. Most of the sprints I contest are uphill, with some flat ones that suit me (since they come off of a downhill last turn a couple hundred meters from the finish). So when I say jump in my biggest gear, it usually means on an uphill finish since that's when I tend to lean towards lower rpms - on flat sprints I tend to sprint in too low a gear. I've also shifted up and down in a sprint, as the terrain changes and I realize I have something left in my legs. Note over.
When I start to lose that acceleration, I usually just keep sprinting out of the saddle. I've hit my max speeds while out of the saddle, so that's what I do. I've experimented, maybe 1000 plus sprints in practice. I'm figuring 15 weeks of sprints (3-4 months), 15 sprints every Tues (leading out every other sprint, so not 30+ sprints), for 5-6 years, and that's just for SUNY Purchase sprints. Then maybe 100 Route 120 sprints at Gimbles, and some crazy number of sprints on my own. I've figured out what works for me, and I'm willing to try outlandish things to make sure they don't work.
If I sit it means I'm dead, can't accelerate, and am hanging on for dear life. Usually it means I've overestimated my sprint, or I've gone from way far out because I thought it would suit me tactically (jump, get a gap, and hold gap to the line). It's very unusual for me to do that, but I've done it in very unusual situations.
If I'm gear limited (like on the track), I have to sit, because I'm not coordinated enough (or practiced enough) to sprint at, say, 160 rpm in a gear while standing and trying to go around only slightly banked curves. So I sit and hit maybe 130 rpm. I haven't sprinted enough on the track to know what my limitations are, but for now it's 34 mph in a 90 inch gear (50x15). Compared to my road sprinting, I've done maybe 25 sprints on the track, and I can't say I've felt like I've done a good effort on any of them - jump too late, can't hold the lower lines on the track, haven't practiced seated sprinting, etc etc etc.
How do you increase your top speed? This is gear independent, i.e. it's not focusing on gearing, it's focusing on top speed and having you experiment with what works for you.
Basically you find a spot that allows you to lead yourself out for a sprint (i.e. a downhill) followed by a sprint friendly straight. Use it as your sprint scale, and work on going as fast as possible. I find that I go fastest by sprinting until I can hit a certain rpm in a gear, then trying the next highest gear. Usually my sprints will be something like this:
1. Jump in a 14, start to lose the sensation of the pedals under you, go to the 13, start to spin it out but you may have something left in your legs, then 12, feel totally bogged down in that last gear. Go around and try again.
2. Jump in 14, then the 13, and when I'm out of the saddle, sprinting my brains out, and I think that I'm pretty well maxed out in the 13, try and pedal faster (not harder; think faster). Go around again.
3. If the 13 worked, then try and sprint until I feel like I'm pedaling faster than I can apply power efficiently. Usually I shift, i.e. into the 12, and get bogged down. Go around and try again. Repeat until legs are fried and the 13 is getting hard to move.
After doing that a few times, it's clear that (in this example) the 13 is good, the 12 is too high. So my goal is to get a 12.5 gear (one that's between the 12 and 13). You can do this because a 1 tooth jump at the high end is usually 10+ gear inches, but if you go 2 teeth smaller on your chainring, it's about a 5% decrease.
Therefore I go home, rummage through my chainrings, and put on a chainring that's about 2-3 teeth smaller (use the same cogs) or larger (use one cog larger) than my big chainring. So I put a 51 on, or a 55.
If it's a 51, I use the same cogs, and usually I can go in the 12 (because now it's a 12.5). Then I work until I want to shift to the 11, but then I bog, then I go back to my normal chainring, and usually I can go in the 12.
If I go to a bigger ring (typically 54, but I'm saving a 55 for some special occasion), then I add a tooth to the above cogs, and usually I can do the 12 equivalent (i.e. 55x13, or kinda sort like a 53x12.5). Then I work on doing the 55x12, in this case.
You can start with a 51 chainring, and when you get to a trouble gear, go 53 (plus 1 cog), or go from a 52 to 54/55.
At the same time, don't be afraid to try something outrageous.
When I started getting into riding, I wanted to know what I "needed" to do to race well. I asked a friend of mine what gear he'd use in a race going up Wolfpit Road in Wilton - it's a steep as heck road, at least one pitch.
49x14 (53x15 equivalent)
What??? I didn't believe him. I'd be in trouble going up in my "fast climbing gear" of 34x21. Luckily, since we had 4 of 7 classes together, I pestered him non-stop for a few months. Then it finally got warm enough to ride outside. I rode the hill in the big ring (48x19) for the first time in my life. Then the 48x17. 48x15. And I did each gear twice to make sure it wasn't beginner's luck.
I finally collapsed halfway up in a 48x14, but I'd done so many repeats my legs were fried.
After that epiphany (I was 14 years old), whenever I felt like I needed to ramp up my game a bit, I'd do some stupid big gear attack on group rides. Any hill under 400 meters was eligible game, and I'd attack up these things in a 53x13 or 12. I'd blow up spectacularly of course, but the point is that I'd try and remind myself that, look, you need to keep an open mind, you need to try weird things, because if you don't, you start limiting yourself.
(This whole open mind thing doesn't work for me for my ftp - no matter what I think is possible "Hell, I'll just go and do 400 watts, I know I can" I just explode a minute or two into my alleged 20 minute effort. So my theory here has individual limitations. But you get the gist of the idea.)
Hope this helps,