The Vice-Presidency is NOT a good place from which to win the Presidency.
In modern times
Eisenhower's VP eventually became president.
Kennedy's VP became president.
LBJ's VP became nominee for president.
Nixon's VP who wasn't indicted became president.
Carter's VP became nominee for president.
Reagan's VP became president.
Bush Sr's VP was universally regarded as a dumbass.
Clinton's VP was elected president but they counted bad.
Bush Jr's VP was universally regarded as Mr. Burns.
So record suggests VP is actually a very good stepping stone to the top job these days. Even if you take assassination and resignation out of the equation. It's not that Cuomo would turn down the offer. It's that he won't be offered. It's obvious that Biden is staying on the ticket. Also it seems clear Biden wants to be the next to use the vice-presidency as a stepping stone to the big chair but his situation may end up like Alben Barkley, though Biden would actually be very close to Reagan age's when winning a landslide re-election.