This comes up from time to time in various forms. The fundamental problem is that we don't want people to be able to "change history", and then claim "I never said that". If we had a reliable way of determining who was a professional, or more importantly, who wouldn't abuse the privilege, then I'd like it, but I'm not sure that we'll ever have that. If we let people pay for the privilege, then we potentially create a class of "trolls with money". The site has always been about fairness and treating everyone equally, which argues against a privileged class. I'd have less of a problem with it being a membership perk, as long as the price of membership wasn't too high.
We could perhaps improve things by making the editing window longer for everyone. I think it's an hour now; if that hasn't been changed recently, but it was longer in the past. This raises the question of "how long is too long". In other words, when does the danger of changing history become larger than the benefit of being able to fix an error? It's possible that we're being overly concerned about the history-changing thing; I don't know about that. We could trial a longer period and see if there are any problems. The problem with all our previous "trials" is that we never have a concrete metric for success or failure, we don't have a good way of measuring things like user annoyance, and we don't have a mechanism for making changes on the basis of user input.
A related minor point involves a shorter window when you can edit the post without it being labeled as having been edited. We used to have the ability to edit for a very short time, probably 5 minutes, without the post getting cluttered with a "Post edited by" message. This is really useful for the stupid typos that you see the instant you press Post. I'd love to have that back, even if it was as short as 2 minutes.