I think the people with the personality to want to be a lead singer also like the “coolness” of being a guitar player as well. So they naturally gravitate toward both.
I believe that John Lennon sang about as many songs as Paul. In my mind at least, that would make it debatable that he was “the” lead singer for the Beatles. He is obviously a bassist that can and did sing lead.
I also think that some styles and songs in rock make it difficult rhythmically to play the bass line and sing at the same time.
Guitar parts tend to meld with the voice part, plus if there’s another guitarist, the singer can even stop playing for lengths of time and have everything work fine.
He still plays bass live. Not on all songs, mostly on Beatles songs.
Rob Zabrecky from Possum Dixon, and… didn’t Brian Wilson play bass for the Beach Boys? That guy from Spacehog did, I think, and Jemaine of Flight of the Conchords often plays bass.
Bassist Benjamin Orr sang lead on lots of The Cars stuff. Sometimes I mix up whether it’s Orr or Rick Ocasek singing, but I know it’s Orr singing “Drive” and I’m 99% sure that Orr’s sings on “Just What I Needed” and “Let’s Go”.