Americans have a deep reverence for their personal brand, but it's worth considering they don't install their government model on countries they conquer. Japan, Iraq, Germany, etc are all Parliamentary.
We can’t fix ours in-place—technically, yes, but practically, no, largely for game-theoretical reasons—so we’re stuck with, effectively, an obsolete constitution. Fortunately, those who’ve set up new states in our name haven’t been forced to install that same known-bad model, so they’ve done better.
It's also a different context. The problem with presidential systems is they become despots. That historically hasn't been a problem in America, because it's a big country with multiple power centers.
Not relevant. The House behaves like a parliament. It's currently hung.
True. Would not help us before November 17th, though.
Also, parliamentary democracies do fall into the trap of back-to-back snap elections. Given the current situation is likely to change within thirteen months, I'm not seeing a fundamental advantage to a parliamentary system with respect to this dynamic.