Looking at defense spending, I do not think it saved so much money. It mostly ensured that the US would be the only major nuclear power in the West - so the "military protection" was more something like a moat for the nuclear monopoly.

And monopolies are something the US loves (think of big tech, Comcast, etc.) and the EU dislikes ;-)

With the US stepping away from its monopoly, it is only a matter of time until more European states will enter the nuclear protection market.