If rock groups were selling most of their music to English teachers, you could expect proper English in their songs. However, their main audience is teenagers. In the Beatles case, at least at the start of their career, their music was written to appeal to British teenagers. You will hear things like "he don't don't have any more time" often in teenagers normal conversations. Also, "don't" kept the beat of the song, where "doesn't" would not. Two points then - the words don't have to be good English - it is more important match that of the people buying the songs. Also, the rhythm of the song must be kept up.

Yep, they do it a lot. But I don't recommend making a habit of it. In a song it sounds cool, but regular use of such patterns does not.