If someone has published libelous statements about you, there are legal remedies for that. If they're insufficient, those laws should be improved.
Your shit does stay with you forever. As it should. Because it's truth. Crafting your own image by using legal means to remove things you don't like presents you as someone who you are not. I find the thought of doing that to be incredibly unethical.
I've certainly posted things on mailing lists (that are likely still publicly searchable) that I regret. I was younger then, and now I'm maybe, hopefully, a little wiser. I would hope that someone seeing something from me posted in the 90s (for example) would think "oh, he was a teenager then, and he's probably a very different person now". And if not... well, I tend not to care about the opinions of people who lack critical thinking skills.
On human civilization scales, the internet is barely an infant. People aren't used to having such easy access to a variety of things about other people's lives. Once we (as a society) gain more perspective on what that means, we'll be much better equipped to make rational decisions about others based on that body of data. Everyone has things that embarrass them. Only very recently was it so easy for others to find out about a lot of those things.