Most of those controversies seems fairly tabloid manufactured. Advocacy for homeopathy isn’t criminal or immoral, just not that bright. The idea that he has untoward “access” is…well, a consequence of having a monarchy. The solution for that is to not have a hereditary monarchy.
Opinion polling in the UK shows Charles is generally seen favorably by a majority of the country most of the time for the last 20 years.
Public opinion of Prince Charles improves in latest royal favourability poll | YouGov
The “embarrassing revelations about his sex life” sounds incredibly American-centric and dated. He hasn’t been unfaithful in decades, has been with the same women since the 90s, is married to her, and she herself is a working Royal. This isn’t 1880, most people understand that people have affairs and get divorces.