See the Help Center article on Accepted answers. Somewhat contrary to the rest of the mission of the Stack Exchange network (to serve as a high-quality information repository), the green check of an accepted answer only denotes that the Asker has found the answer useful personally. That said, I do think it's worth encouraging; there's already a reputation bonus for both asker and answerer, and (limited!) commenting to encourage voting/accepting is generally considered fine. See also https://meta.stackoverflow.com/q/313206/10495893. (These last two links are from meta SO, but I think are still relevant.)
So those type of questions keep up popping forever and looking for an answer.
This should be unaffected by accepting answers? Someone who searches first should find the good answers with or without the green check, and someone who doesn't search won't find the answers either way. If folks ask a duplicate question, it should be closed as such (and you the close-voter can upvote any answers on the target question!), not answered again (well, if you have something to add, do it, but on the duplicate target; and if it's not applicable there, then probably not a duplicate).
I wanted to know how prevalent this really is, so some SEDE queries:
https://data.stackexchange.com/datascience/query/1803434#graph
! I really ought to have cut off the end time; the most recent questions may still get accepted answers later. Please ignore the rightmost part of the plots.
Acceptance rate among answered questions by month, on DS.SE:
The same on StackOverflow:
And finally CrossValidated: