I’m guessing the current price has to pay for a whole new rocket, as NASA probably won’t use a used (“flight-proven”) one for humans.
Eventually I expect used ones to be not only cheaper, but also more reliable. Like for (water)ships - they say “it’s new after you’ve owned it for a year”, the implication being that you spend the first year discovering and fixing manufacturing defects.
What happens to the rockets after they're flown for a single mission? Do they belong to SpaceX for later re-use in commercial cargo missions, or does NASA own them?
NASA pays for the mission, transport XY amount of tonnage to the ISS. The rocket remains owned by SpaceX. In majority of situations, owning a rocket means little as it cannot be reused. Also very few customers have the means to "run" a rocket, NASA fits the bill and it's conceivable NASA could buy a F9 and use it after quite a bit of training, but this makes little sense for them and little sense for SpaceX.
I think I'm picking up from context (aka reading between the lines) that the optics of NASA using a refurbished rocket - and it failing - is not good, so let SpaceX do what they want.
Recall that a lot of aerospace budget from the US is defense spending dressed up as something else. Similar to the way the original space race was a proxy war for a proxy war: If you can fly people into space you can fly an ICBM to Moscow/Washington DC.
Eventually I expect used ones to be not only cheaper, but also more reliable. Like for (water)ships - they say “it’s new after you’ve owned it for a year”, the implication being that you spend the first year discovering and fixing manufacturing defects.