It does not matter. One does not — or, rather, should not — have a right to forcibly alter other people's memories or perception of himself
Even if those perceptions are wrong? I'm not completely convinced you are grasping the long-term impacts here. If one single mistake can ruin your future life, with no hope for redemption, well, you've heard the saying "In for a penny, in for a pound"? Why stop at a small misdemeanor when you'll get the same effect (a ruined life) for murder?
The reason it might be a good idea to allow these to expire from search engines is because the internet has greatly improved the global recall. Previously, this sort of offense would only be known to you if you personally knew someone who knew the individual. These days, you can jump on google and find out all sorts of random things about any individual you get a name for... and the internet will always remember this!
I'm guessing that you think that you'll never end up on the wrong side of an accusation, or never have any incidents that affect your future employment recorded on the internet... With the growing surveillance and online records, I don't really share that same confidence, for either myself, *or* you.