They didn't have many mics, and they certainly didn't have multi track recording. They either mixed live to stereo or for a lot of pop song recordings they recorded on three tracks, with the vocals on a track of its own and the rest of the band mixed live to stereo on the other two. Then a very rudimentary mixdown was possible, to get a final perfect balance of vocals against backing.

I don't think analogue vs. digital is much of an issue. Good analogue tape recording equipment existed in the 1950s but it was hugely expensive (same applies to mics). One consequence of that was that the few engineers who got to use that equipment tended to be highly qualified, very technically knowledgeable, not only about electronics but also about acoustics, and had very good ears. That's probably the main reason why they made good recordings.

Anahata