Trump was never taken to court because the position of the Justice Department is that the President is above the law. That could be changed.

The Senate was not equivalent to a jury since juries do not generally have the same incentives to pervert justice that the Senate did.

> ...why not literally every other government position?

The President has dramatically more power than almost any other government position. That being said, I could see it being required for Supreme Court justices and members of Congress.