I’m not sure this counts as a musical collaboration or not, but according to a documentary about music from the James Bond movies, the producers of the films approached Amy Winehouse about singing the title song of one of the movies prior to her death. I couple totally imagine what it would have been like to have Amy belt out a Bond movie title song.
There is also a category of collaborations you wished happened before the collaborators were too far gone on drink and drugs to produce anything remotely listenable
E.g. Hendrix and Jim Morrison did indeed collaborate but in their “far gone” stage 
in the bootleg recording of their collaboration you can hear someone say “Jim, the microphone is over here”. It’s not all that
If I remember correctly, they did encounter each other when Beethoven was still a teenager. As I remember the story, Haydn had a pupil (Beethoven) who he knew was going to be prominent, and invited Mozart to come see for himself.
Also: We do in fact have an example of such a pairing, Mozart’s Piano Sonata #20 in D-minor. The cadenza (one of them, anyway) was composed by Beethoven and sounds for all the world like a mix of the two composers. It’s my single favorite recording of Mozart’s music.
I also like the version of “Love Ain’t For Keeping” with West better than the one on “Who’s Next”. It’s on the extended CD version of “Odds And Sods”.
In 2003, the Doors actually did a reunion tour, with Ian Astbury on lead vocals. (I saw them live in LA and it was one of the most amazing concert experiences I’ve ever had.) There was talk of them recording a new album at the time, but a legal dispute barred them from using the Doors name and nothing ever became of it. I wish I could’ve heard that album.