I don't think it has to do with legato, at least not in the way ecline6 suggested, because if you're using 4th finger for the top d#, the f#-d# stretch would still be a problem (at least it's for me), and the switch should be marked on the first beat instead of the second. In fact, the only working fingering for using 4th on d# I can think of is to use 1-1-2 for the triplets.
Instead, I think the reason is that if you play g# with the 3rd finger and want to keep the triplets legato, you might have tension in your hand when you play the e octave. With the switch that doesn't happen. Still, it seems to be unnecessarily complicated. Just use the pedal and make sure you don't swallow or accentuate the g#.
Btw, the reason people use lots of pedal is probably because that's what Beethoven wrote! In the beginning it says sempre pp e senza sordini, which means all the time very quiet and without dampers (i.e. with the pedal down). On a modern piano you have to change the pedal at least partly every now and then, though, since the sound is longer. You actually get a pretty cool effect if you, for example, don't switch the pedal at all during the first two measures.