If people in positions of power fail to avoid the appearance of impropriety, they erode faith in the system. That leads to very real corruption, even if the original acts were ethical.

And from a practical standpoint, any honest politician should want to avoid it, if nothing else to avoid arguing about bullshit from a defensive stance. So there is very much an argument that smoke needs careful fire investigation.

The next step down the this road, of course, is arguing that people are above reproach precisely because of their position. "When the President does it, it's not illegal", etc. Corrupting a government is a process, if you look at other corrupt countries, comparisons are an easy way to sort of spot, "you are here."