In a band that's just starting or hasn't peaked yet: whoever the principal songwriter is. Otherwise, yeah, the singer. It's not 'impossible' to replace them, but it certainly affects the product more IMO. Someone mentioned Brian May earlier, and that reminded me of a comment he made on Absolute Radio two years ago: the lead vocal is the core of a song; everything else is important, of course, but without a strong lead vocal you're just wasting your time... and that's coming from a lead guitarist.
A good lead vocal is important but the music behind it is just as important. I've never liked a song that had great singing/lyrics and "just ok" melody/music. In fact, I've liked the opposite. So for me the music wins out. A good vocal is the the stitch that closes it all together. You have to have it, but you can't rely on it for everything.
Aerosmith without Perry: it happened, albeit briefly; Aerosmith without Tyler: IDK if it's ever happened, but it'd be much weirder IMO.
I'd never imagine Aerosmith without Perry again.... Just listen to Rock In A Hard Place (the album). The soul and the heart of the band was totally lost with the Perry-less Aerosmith. It was horrible. However, the Joe Perry Project was great. Let The Music Do The Talking (Quite funny in this case! ) was an awesome song. I don't like 1 song on Rock In A Hard Place. So in this case, I'm throwing the bone to Joe. That said, I love Whitford, Hamilton, and Kramer and think they are underrated. But an Aerosmith without Joe is just not for me.