There exists a concept of "American exceptionalism" [1], which describes this popular belief that the US are superior. It also probably goes with the fact that it is a very big country sharing one culture, and it is easy to not spend too much time looking at what other countries are doing.
> presidential democracies where presidents are elected by popular vote are a disaster
I would like to add France to the examples supporting your case: in the first round, Macron got less than 20% of the votes, and a non-negligible part of those was already trying to be "efficient". As in, the people would have voted for someone else, but they voted for Macron because it seemed more likely that he could win against Le Pen, the far-right candidate.
This means that less than 20% of the people (those who voted of course) wanted Macron. On his first day, more than 80% didn't want him. Still he behaves like if the French people wanted him.
> by having the parliament elect the president
An example I like is Switzerland: they don't have a president at all. They elect their parliament, and the parliament elects the Federal Council made of 7 people from the main parties.
What this means is that the executive power is a consensus by construction, and most of the people is represented (because the Federal Council is made of the major parties, which represent the majority of the people and go from left to right).
Feeling represented is very important: when the people does not feel represented, they take out to the street and protest. I don't think it happens as much in the countries you described (Germany, Italy) or Switzerland.