The mere fact that most people feel that way shows, to me, that the system works. Compare that to e.g. France where Macron got less than 20% in the first round. It means that 80% of the votes were not for him, and of the 20% remaining, a lot did not want him but just thought he was the best chance against the far-right candidate. Right when Macron was re-elected, you could say that more than 80% of the people who voted did not want him. That's a problem IMO.
Not even talking about the US presidents...
49% minority = get fucked
<1% minority = here's your new lords and saviours
The opposite (again IMO) is a system where the people votes for a president every 4 years, and invades the Capitol when they lose. BTW Switzerland does not have a president, but instead a group of 7 representing the biggest parties in the country. So there is consensus even at the highest level.