Also the traditional barbershop quartet for acapella.
Interestingly, I like the 5-piece versions of all 3 of these: add a keyboardist to the rock band, a piano or harpsichord to the classical string or woodwind quartet, a female vocalist to the acapella group. Having two leads lets you do much more intricate countermelodies and harmonies.
A string quartet consists of 4 tonally adjacent instruments, and is thus much more like 4 humans talking.
A "classical" rock band consists of 4 utterly different instruments from a tonal perspective, and is thus nothing like 4 humans talking. Same thing for jazz - and its why you can have multiple instruments performing simultaneously and in ways that are not obviously connected to each other.
"Music for 18 Musicians" by Steve Reich is probably one of the masterworks of the second half of the 20th century.
Any vaguely disco-adjacent band will have more than 4 people on stage because there will be at least keyboards and horns in addition to drums, bass, guitar and vocals. Even a band that simply adds an additional person player percussion to a typical 4 piece exceeds your limit yet can wonderfully enhance the music.
If you haven't seen any of those bands, then that's your loss, but provides no reason to try to generalize about the right size for a live band.
Vocals are often a person who is also playing an instrument. So in a 4-person band you can have up to four voices, lead and rhythm guitar (or maybe keyboard), drums, and bass.
Edit: I thought you linked to yet another famous band. People keep doing that... 99% of bands a normal person would see in normal life don't even have a wikipedia page.
However your link looks about jazz.
A common rock band is rarely good with more than 4 members because people lose unity and it's just technically harder and people are rarely professionally trained.
Honestly I wouldn't know anything about rock bands because I don't listen to it at all so you could be very right. I just responded because this thread was talking about string/barbershop quartets, which are almost definitely 4 parts because that is the minimum number of people required to make a 7th chord, and then again because you didn't know what a Big Band was, which I suppose is very understandable, but as somebody that grew up around and playing on them it's super foreign to me.
