PSYCHO was the movie that changed this practice. Theatre owners were afraid at first that they would alienate patrons with this switch, but Hitchcock knew that the power of the film resided in shocking the audience first with Marion and Sam on a hotel bed, half undressed, in the middle of the day, and then the further shock of Marion's murder. Stars did not get bumped off that way back in 1960. Movie goers went along with AH's request, and theatre owners adopted it as a permanent change. But from what I can tell, it was originally just a one-shot gimmick with PSYCHO.
Up intil they closed in the 1990's, a person could still the old-style experience in the Chinese movie houses in NYC. The films played continuously and you could go in at any time. This was true of the grind houses on 42nd Street as well, but they faded much earlier.
Brian