That's it, spot on, Funny Paper. The mono mixes were the best central "picture" from what were 2-track tapes in the beginning, moving up through 4-track, 8-track, etc. The stereo mixes were about placing those individual tracks within the "picture".
The reason there is no true stereo mixes of some songs, eg. She Loves You, is because the studio master was destroyed after the mono master was created, leading to all stereo mixes actually being "fake" stereo produced from the mono master - where, generally, they weight the high end to one channel and the low to the other. This is ...