I’m getting flashbacks to Stack ExchangOverflow, and various attempts to encourage people to accept answers on their questions… from memory, every attempt in that direction fell foul of the simple problem that nobody likes to be told what to do, and hit-and-run posters aren’t going to come back to see your admonition anyway.
There are settings to allow admins, mods, and various other high-value personages to tick “solved” on a post, and I think that’s about the best you’re going to be able to get.
We do this quite a lot on one of my sites. I’d say 80% of the content is “questions” or “issues”, and our mods are quite quick to mark topics as solved. We only started using the solved plugin this year, and we’re starting to see more users mark their own topics as solved. I think it’s just a matter of reaching that “critical point” where people know what “solved” is, and they start using it themselves.