OMG, the ambience of the reference totally changes if it were to be a reference to Mickey Mantle.
There's simply more to it than just best fit of syllables.
Come on, and the reference to "Boo-hoo hoo"? Remember, Joe DiM. was first and foremost, a modern era guy, being the star athlete who marries the prize wife (Marilyn Monroe)! Then upon her death, becomes the epitomy of loyalty and fidelity - virtues at the heart of the song written by Simon. Remember, the same Joe Di. who would send a dozen roses to Marilyn's grave three time a week and would never speak of her to the press, and never remarried.
Mickey Mantle totally changes the meaning and loses all that level of meaning. Using Mantle reduces it to a juvenile, knuckle-headed level, imo.
Honestly, I think this is a significant moment of self-reflection by a renowned bard speaking to his generation in one of the most popular and accomplished songs of an era. Simon hit it out of the park with referencing Joey DiMaggio, and i think his comment to Dick Cavett was only part of the explanation (in that it does sound a lot better than the alternative).