That's a fair position to take but I don't think it will ever be the case that sleaze from public figures is not reported on.
To some degree, that is what they sign up for and the price of fame/the huge rewards they enjoy.
In fact, not behaving in such a manner is something that their employers and the people that givevthem such rewards also expect of them. David Mellor, many other mps, Jamie Theakston, Frank Bough and many others found out that their employers also (at least temporarily) considered their behaviour a serious matter, not just the media.
And there is a good argument for having some sort of implication that, as a public figure, you do not fall into disrepute is a good thing. Especially in the era of scumbags like Trump and Johnson trying to degrade public standards.
It is also worthwhile stating that many people who are not in the public eye and wouldn't make the front pages - eg judges, doctors, teachers, etc - would also find their profession and reputations in serious jeopardy if caught in the same position as Edwards, even without the media coverage.