> it's unclear that Nasa can ever be without that (military and political) oversight
By design, Nasa is probably doomed to get interference.
> If theyd kept their budget and autonomy after the moon landing it looked like they wouldve been building reusable rockets
Pure fantasy. Nasa's interest for reusable vehicles led them to the Shuttle. Even without all the design changes, it would have been a dud.
Due to its nature, Nasa can't freely explore and commit to a design like SpaceX does/did. It draws a concept and freezes it after contractor review, only to find after an already massive investment if it works. Then there's public accountability instead of executive risk taking.
I'd bet the proper way to have protected Nasa would have been to keep it focused on key scientific missions with limited financial exposure. Mars rovers are a perfect case, or most James Webb.
Using Nasa to go back to the Moon or reach Mars was doomed to fail (sort of like it failed post Apollo).