I'm afraid to be repeating an idea that might have been proposed before. It seems very natural and wanting implementation
I'd like to see a button in the results screen that would propose the players remaining at the table to play another game, but not with another random set of cards, but rather with one that would simply replay the kingdom of the previous game.
It is often that when I play with friends, we hit a game that we really enjoy and that we think very rich in possibilities. Often, one of us comes to the conclusion that their game could have been much better (more successful) if only they didn't buy the cards they did on their early turns. It would be so fun to be able to verify those claims.
I know that we could remember what cards the kingdom featured and simply set a table up manually, but... I mean, what do we have the computers for, right?
And besides, I don't think it completely out of the question that even in a game between strangers, they both might fancy giving the set another go to see who comes out on top that time