The big thing that you can accomplish by raising your body and moving it forward is you can tilt your pelvis forward. This allows you to have a flatter back without doing any kind of stretching etc. A good example of this that everyone can relate to (at least find a picture of) is Jens Voigt. He has a very forward position, very high, and it allows him to get pretty flat on the bike. His set back is significantly less than someone like Tom Boonen. I forget the numbers off hand but the difference between the two is 3 or 4 cm, something like that.

Also for time trials a higher and more forward position works well. It allows a flatter position (more aero), it gives you power, and it doesn't cramp your breathing as much as a lower, more rearward position.

Why flatten your back if you're not racing?

A flatter back gets you a few things. First it is more aero so it's more efficient. Once you're going about 20-22 mph it starts to make a difference and most people can ride that speed on a flat road. Second it puts more weight on the front wheel. That's better for cornering but it also relieves pressure on the saddle, making the bike more comfortable over longer rides. Third it allows you to recruit more leg muscles while pedaling. Your body naturally wants to recruit those muscles - when you're climbing a hill you instinctively lean forward, not for aerodynamics but in order to recruit your powerful glutes and other less used muscles. As a racer of course it's important to maximize available power but as a recreational rider it's simply easier to ride.

I fit a lot of riders in the pre-everything-computerized days. I did it based on experience and feedback. Some of the riders that I recommended a forward/low position were recreational cyclists on hybrid bikes. They complained of saddle discomfort, difficulty on hills, and "too bumpy" a ride. By taking these riders, moving some weight forward, recruiting more muscles, the bikes somehow got more comfortable, easier to pedal up hills, and their butts weren't numb or sore in 5 minutes. As a bonus their knees didn't hurt as much, they had less shock traveling through their backs, and their bikes were more stable overall. Those riders recruited more of their cycling muscles, enabling them to get stronger, creating a great cycle of improvement for a while.

Drawbacks include an initial period of adjustment/conditioning/discomfort in your neck, shoulders, and arms, as those bits have to work to support your head more. You'll also need to condition less-used pedaling muscles - mainly your glutes and different parts of your quads and hamstrings. Another is simply accepting that a lower position isn't necessarily bad for a recreational rider. You'll need to stay with a narrower saddle (wide tractor-like saddles only work with upright positions; many entry level hybrid bikes come with sofa-like saddles not appropriate for a higher and more forward position). Finally you'll want multiple hand positions on the bars (more weight on the hands means having more positions is important).

I fit a friend of mine (racer, teammate, friend) who had been "fit" at a bike shop. He'd just gotten into racing, he had started to develop those cycling muscles (glutes, lower back, shoulders, neck, etc), and he asked me for feedback on his racing, position, etc. He'd been frustrated at the local Tuesday night training race series as he didn't have the power to break out that win - he'd get second or third but he was clearly slower than the guy/s who were beating him. I made some wholesale changes to his position, a couple cm here, a couple cm there (raised saddle 1.7 cm, forward 1 cm, dropped stem 2.5 cm, extended stem 2 cm, so net difference 1.7 cm higher saddle, 1 cm more reach, and 4.2 cm more drop to the bars). Basically he went from low and back to up and forward. Without any time to acclimate (it was one week to another) he won the next three Tuesday night training races he did, each by a clear margin, like by 40 or 50 feet. Fitness-wise he was the same - just his position changed. He found he could turn about one gear higher on the flats. His bike inspired confidence in the corners, with more weight on the front tire. He also placed in one of his goal races, a very difficult race (I did it once, finished off the back).

(On a related note he had a sudden tire failure mid turn later on. He stayed upright without any problems. I attribute his having more weight on his front tire as a factor in him not going sideways at 30 mph since he hasn't done any kind of handling drills.)

So a more forward, higher position has benefits, even if the overall leg extension isn't different.