Why descend?

If you're wondering why people might want to descend off the bridge, one reason is just the for the sheer challenge of it. But more importantly, there are plenty of ways it can be exploited.

Hey buddy, seen any aliens around here?

No more enemies

By descending off the bridge you skip the trigger for the first ground battle, and because of that, no enemies will spawn in the rest of the level yet. If you want, you can go all the way to the final cutscene completely unaccosted - though you'll need to use a Banshee at one point to skip a locked door. That's a boon for speedrunners, and at the very least it's a novelty for the rest of us. It's quite odd to see the place deserted for the first time.

Rearranging things for novel play

But if you're interested in fighting covies or enjoying various mischief, the real benefit is that you can move things around - Banshees, Ghosts, Shades, a Wraith, and weapons - so that when you come back later and resume normal play (which is easily done), things play differently. You can engineer novel situations that way.

Handy toy for the first ground battle

One of the simplest things you can do is bring back a Banshee or Ghost or the Scorpion to the area below the first bridge, so you'll be able to use it as soon as the first ground battle kicks off. You'll find that idea detailed in New toys in the first snow battle, and I mention many other bits of fun in my general article Rearranging the furniture.

But the meatiest applications are in the spiral path megabattle and twin bridges megabattle. In particular you can set up blockades in advance (e.g. a line of Ghosts), making things significantly different, and you can also leave spare weapons around to give yourself more ways of fighting the battle. There's a lot of creative potential there.

Some of these things can also be done by skipping certain later triggers (though not necessarily with such ease), but skipping the one for the first ground battle is usually the most convenient way. So getting down off that first bridge is an extremely useful thing to be able to do!

Tricking

A descent can also be used in starting off the work for various tricks such as getting an extra Warthog, getting two or three extra Marines and a hog, or getting seven extra Marines and a hog.