Technically, the combination of government and corporate power is fascism.

It would be borderline for him to make changes to NASA that benefit him if they are improvements. It would also be par for the course for government officials. It will look bad no matter what he does with NASA. If he shuts them down, he's killing the competition. If he makes changes that benefit him, it's corruption. The smart thing to do is give it to another department to deal with, but I doubt Elon cares if he looks bad.