It wasn't just the music with the Beatles, it was the whole image/youth culture/pop phenomena that they opened up. It's doubtful any of the other British Invasion bands could have pulled it off on the level that the Beatles did. Music wise, you still had the Stones and all the other bands based on the blues scene in London, and quite possibly that movement would have taken root in the US. But without the Beatles moptop image to pave the way, bands like the Stones and the Kinks might have appeared too far out for that time period.