A “solved” problem might have a better solution that one should be able to add after the initial solution is accepted, so closing it doesn’t seem like the right solution.
One could tag a post with a “solved” tag (or maybe edit the title to add “[SOLVED]”) to mark the entire topic as solved.
I guess it can’t hurt to install the plugin and see how it goes. Unless there is an objection, I’ll ask the system admins to install it.