Doing "stupid space stuff" in no way prevents us from improving things. The NASA budget is not even a rounding error in the grand scheme of things. And getting rid of the nazi nerds is an entirely different conversation.

We spend on space research about 3% the money we spend on military. Is this really the priority?

The money spent on the Apollo program wasn't all packed into a suitcase and taken to the moon, it was spent and reinjected into the economy. In particular, some of it went to the wages of some of the most highly-skilled, best-paying jobs that women and black people could get in the fifties and sixties, and that did a lot of good directly, before we even get onto indirect effects like inspiring generations of people to pursue a career in STEM subjects or developing technologies that would be used elsewhere.