As I mentioned in a top-level comment, you can use robots.txt to disable Internet Archive's (Wayback Machine) archiving of your site. If you dislike your site being archived, I suggest you do this. Their intention is not to be a monster of the Internet who embarrass creators against their will.
One solution to this might be to maintain separate archives when a domain changes ownership, based on WHOIS information. Previous owners could still request deletion via email as is currently possible.
