You seem to have some misconceptions about rechargeable batteries.

NiMH and NiCd cells start at about 1.4 volts and go down from there. 1.2 volts is the "nominal" voltage given for them, but they start higher -- and really, once they hit 1.2 volts, most of their energy has already been used. As you said, alkalines start at 1.5 volts and go down from there. The "nominal" voltage is given differently for primary and rechargeable batteries. (Why, I do not know.)

But it's not that simple. Rechargeables tend to have lower internal resistances than alkalines, which works better for high drain devices. (Like bright lights on high settings.)

As for 18650 batteries, their nominal rating is 3.6 or 3.7 volts, but they start at 4.2 volts. Yes, three alkalines would start at 4.5 volts, but the *significantly* lower internal resistance of that 18650 over 3xAAAs will mean that if you're using the light described earlier on high mode the light will be *brighter* and stay brighter for longer (due to the larger capacity) than it would with your alkalines.

Also, you seem to be confused about the relationship between voltage and light emitted -- you seem to be assuming that it's linear, but it's often not. For example, with an incandescent light, the energy consumed is proportional to voltage *squared* assuming that the resistance stays the same (which it doesn't, just to complicate things.) And to further complicate things, the efficiency (amount of of visible light emitted per power used) typically goes up as the power goes up, as the filament gets hotter. In the case of an incandescent light, a small reduction in voltage usually leads to a larger reduction in light output.

As for LED lights, it depends. The better ones have regulators that keep the light output fairly constant over a range of voltages, and the cheaper ones are fairly linear with voltage as you suggested -- but things do vary.

In any event, people who use rechargeables often aren't after the maximum possible brightness. Instead, they're looking to save money and reduce waste. But if you keep your batteries charged, they'll likely be brighter than the alkaline batteries that you keep using until things get dim because you don't want to throw out batteries that are only 1/4th discharged.

Good bicycle lights (ones that put out a lot of light) use a lot of power. Alkalines could be used, but it becomes expensive. Rechargeables (or a dynamo) are what makes it cost effective to use a 400+ lumen light. If you're forced to use alkalines, you'll probably opt for a 50 lumen light instead to keep your costs down.

Um, the real replacements are here now. NiMH cells are largely drop-in replacements for alkalines (with a slightly lower voltage at first, which most lights handle just fine, as being designed to deal with alkalines and their always dropping voltages) and while Lipo and li-ion batteries generally aren't drop-in replacements, they tend to be superior when lights are designed to use them. Lead-acid and gel cel batteries are largely obsolete for the purposes of bike lights, but they still worked pretty well.

Hey -- 1995 called, it wants it's CD player back. Today, most music players come with rechargeable batteries. But even with that CD player, NiMH cells will work great in it, I don't know what your problem was. (And really, a dollar an hour for batteries adds up fast for listening to music!)

Motorized toys are exactly what NiMH cells work great in. Their lower internal resistance is important for high drain items like that, and the high drain also means that neither battery lasts long -- which gets expensive with alkalines.

Also note that today's NiMH cells are considerably better than the NiCd cells of "years ago" in most respects. NiCd cells had somewhat lower internal resistances and self-discharge rates than NiMH cells, but the new NiMH cells like the Eneloops have given NiMH cells those advantages and then some.

For a "blinky" tail light, I'd say go ahead and use alkaline batteries unless it's a really bright one. For example, a Planet Bike Supeflash lasts 100 hours on alkalines -- that's pretty good. But 3xAAAs wouldn't even run a 400 lumen headlight for a full hour (or if it did, it would be way below 400 lumens during most of the hour) -- you'll want to use rechargeables for that, or if you must use alkalines, use a much weaker light.

Edit: I've got what looks like that same headlight from DX. (Maybe it's the same, maybe not.) They claim it's 3 watts, but I think it's more like 1 watt and 50 lumens when comparing it to other lights. I haven't tried to measure the actual current draw, however, and don't have the equipment to measure light output (beyond comparing beam patterns with my eyes, of course.)

3xAAA alkalines (good ones) would contain at most about 4 watt*hours of energy total -- so if your light really did use 5 watts, it would last less than an hour. A single 18650 holds about 9-10 watt*hours of energy.

I don't really think they'd make a real 5 watt light that uses AAAs -- AAAs would have a hard time sustaining that level of current draw, though NiMH cells would do better than alkalines.