These are good questions. Although I have no personal animus towards Trump, I can think of three reasons why barring him from future office -- had that been the verdict of impeachment -- would be consistent with our democracy, while other cases you mention may not be:

1. The decision would have been retrospective. He'd be convicted based on things he had already done, rather than things he's expected to do

2. The decision would have been made by a separate branch of government. If we assume -- which admittedly we don't have to -- that the Legislature and the Executive are not vying for power, there's less cause for fear that a person would be banned by his political opponents so that they could keep the power to themselves

3. He's an individual, which leaves many people with his political views (such as they are) eligible.