I think the key with Trump is that he literally doesn't seem to understand how the political system works well enough to have ambitions in regard to it. 1
that is, it isn't precisely that Trump doesn't care about his legacy. It's that he is incapable of understanding how anyone other than himself would see his legacy, or of getting from that understanding to actions.
the virus is a good example. most politicians would understand that you want to ensure reelection by defeating the virus and helping people economically. pretty straightforward!
Trump on the other hand seems to have seen the virus as an unfair personal affront, which nobody could or should really care about, because if they did it would inconvenience him.
his utter unwillingness/inability to engage with a reality outside his own inflated self opinion means the only goals he can really pursue with any consistency/competence are straightforward self enrichment. anything else is beyond him.
like, he wants to be on Mt. Rushmore. He wants to be beloved. He wants to be seen as the best president in history. Normally goals like that would lead presidents to try to defeat a deadly pandemic!
but he just can't get himself to understand that his constituents' well being will affect their view of him.
so...I don't think the problem is ambition, so much as it's his sweeping emotional and intellectual incapacities.
like, Trump sort of vaguely gestured at paying attention to the virus because people around him were telling him over and over that he should and it was an opportunity for those television updates he was doing and egregious sycophantic flattering.
but then people weren't flattering him enough and he got bored. and he never really saw the point anyway.
it's hard to sustain an interest in changing the world when you basically believe that whatever you want to be true is true anyway.