This often had more to do with adopting a system that has some familiarity to the conquered country. In the example of Japan, allowing an emperor as a more permanent figurehead.
That’s not the reason that we spent the 20th century installing governments that look conspicuously unlike our own: it’s that the US model has been known to have several severe, practically irreparable flaws for more than a hundred years, among the kinds of people who study governments, and those same sorts of people had some say in how we set up new governments, and evidently not a lot of pressure on them to make those look like ours.
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.
> the US model has been known to have several severe, practically irreparable flaws
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.
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.