How much of the apparent nimcompoopery of presidents is actually a result of their choices being constrained while in office?

I think that is a lot of it. But there is a related bit too: even when the candidate makes the rational choice (against tariffs for example) they have to frame their choice in a way that minimizes the political cost they pay to the people who think you can run a 1st world economy by forcing the 3rd world jobs to stay here. So even when they make the right choices, they still have to sound like idiots to keep their political reserves from depleting.