You think Ainge did out of spite for the Jazz, to rub it in further? Crowder was the obvious choice to trade because Hay was taking his place not Bradley's.
Ainge isn't dumb. He knows that Bradley is going to be able to sign a big deal next year, and he won't have the opportunity to match it. Crowder is on a Cheap contract for 3 years. He is playing the long game, not just for this year. Crowder is a much better piece to keep because of his contract. He also got a stretch 4 on a 2 year deal for another Cheap contract.
I don't think this trade makes them any better, but it makes sense. They don't need a protected first, which is the most the Jazz should have given up for Crowder.