George Martin always said that he recorded the first two Beatles albums with the extreme vocal/instrumental separation in order to create better mono mixes. He even tried to do the same thing on "Rubber Soul". Both of the first two albums were recorded on two-track machines (they started using four-track with "I Want To Hold Your Hand" in late 1963), so doing a decent stereo record would have been quite difficult. But back then, the Abbey Road producers really weren't concerned with stereo, as mono was the standard of the day. Martin realized that by putting the vocals on one channel and the instrumentation on the other, he could more effectively mix the vocals into the song. He has said that he never intended the two-track recordings to be heard in their stereo form, which is why the original CD releases of their early albums were available only in mono.
I'm sure many other producers of the day had the same idea, which is probably the reason for vocal/instrument separation.
On a side note, unfortunately, multitrack stems of the Beatles' pre-1964 material no longer exist, as Abbey Road policy then was to reuse tape. Some songs, such as "Love Me Do" and "She Loves You" only exist in their mono master form. Therefore, there is no way to do a clean remix to make these songs true stereo, and even if there was, the parties involved would probably never allow it, as they prefer to keep the original mixes, save for special projects like "Love", the "Yellow Submarine Songtrack" and "Rock Band".