Nope!
1) If I were to catch a 62 HR ball or another historic HR ball, and the player didn't ask for it, then I'd keep it. Judge will FOR SURE ask for #62. Means it means something to him.
2) Players keep important balls, bats, stolen bases (see Rickey Henderson) all the time. Of COURSE these mementos are important to them.
3) Cooperstown doesn't just get every important thing. The player keeps what they want.
4) I ALSO am not telling others what to do here. I said what I would do. It IS the right thing to do, but I'm not demanding that others do the right thing. I spell out the right thing, and then others can either do it or not.
5) Now, Judge SHOULD give a fan something for the ball, BUT the order of events should be...fan gives Judge the ball with NO promise of anything in return, and THEN Judge gives fan something.
6) I'm not so sure that ball will be worth THAT much anyway. Will be an American League record and a Yankees record, so certainly it will have SOME monetary value, but will it be worth MILLIONS of dollars? It only takes ONE person to make it worth that, but I'm skeptical that that person is out there.