Anthology 3 came yesterday. Lennon was keen to have "What's The New Mary Jane?" on the White Album. It's a bit of a mess, but certainly miles better than "Revolution 9," the only "skip" track I have amongst their regular releases. Finished Disc 1 while working out: pretty decent to have if you are a Beatlemaniac!
You're right, "What's The New Mary Jane?" might be the stupidest song they ever did after "Revolution 9." It was all part of John's desire during this period to be as outrageous as possible. Yoko's influence, of course.
John is one of my heroes, but he did try at times to be weird because he thought it would impress Yoko. As a reviewer mentioned on Rhapsody when discussing Double Fantasy/Milk and Honey: has anyone ever listened to Yoko's tracks more than once? That's too much for even yours truly, LOL!