Is there any point to stars once you have gotten all the gifts?
No. It appears that stars are only used for accessing new cups and tour gifts. At the end of the previous tour, the star count reset and stars obtained during the New York tour didn't count toward anything anymore.
I kept racing, and eventually if you get another star after you have all the gifts, a message comes up telling you you can't get any more stars past the limit (I'm guessing the limit is getting all the tour gifts), and you get 100 coins instead.