Well, I think the OP has the answer he asked for (though maybe wasn't looking for) - people record bands every frickin way imaginable, for every reason imaginable.
I think that theDAWstudio has a good point in his objective, omniscient, post: a lot of times the way we record a band is controled by constraints - equipment, studio space, competence of the band, band members playing multiple instruments, people's schedules, whether band members live in the same town, state, country. I assume that this is what Beat Poet meant when he said that recording one track at a time is "efficient." Probably the better work is "flexible." Recording the whole band at once is far more efficient in terms of time. The Beatles recorded their first album in a single day - three three-hour sessions. Try doing that one track at a time. (Yes, people in our mid fifties always bring up things like this.)
I also like Bigtree's point about the artistic advantages of going one track at a time. The precision of click-based music is now central to electronica, synth-pop, metal, hip hop. But in some of these genres the precision itself is an artistic end (Bigtree is eloquent about his feelings on this). In others, it's just a means. Metal started out in the early '70's as a loose, sloppy genre and then tightened up when people wanted to record multi-layered guitars. Hip hop is sample based, so it is technically natural to tie everything to a click, but I don't know that there any real artistic advantage to it.
But there are genres that - at least to me - don't benefit from precision: acoustic music, folk, country, blues, funk, R&B, and rock genres that flow from these. They are at their best when they have a groove that comes from genuine ensemble playing. This is the stuff that I like best, and I've build my studio so that I can record a full band in this way. And, yes, I often run into some of the constraints mentioned above and have to one track at a time.
Now we have not talked about the bad reason to record one track at a time: because the producer/engineer is an anal retentive control freak. When I turn on the radio, I hear a lot of stiff, stilted, mechanical music made by studios that were not under any of the constraints listed above. They just valued the studio over the musician and wound up with mass produced music.