That was part of the reason, but it wasn't called crossfade, it had another name, like stereo speaker simulator or something.

Crossfade is DJ mixing one song into the next song.

The speaker simulator makes it so that listening to headphones, your left and right ears get mixed together a bit, with the mixed signal from the opposite ear slightly delayed to simulate the farther distance an audio wave would take to travel to the other ear.

This isn't really just for Beatles, although they're a great example. Certain Beatles songs (not the earlist songs which were mono, but rather the stereo songs from a bit later) were mixed with all of the instruments and voices hard-panned to one side or the other, making them interesting to listen to on speakers, but difficult to listen to on headphones. The speaker simultator feature let you listen on headphones and hear them like they were on speakers.