Inspired by is welcome
I don't see any problem with posting questions inspired by known solved problems, where the answers will not just be the known solutions copied and pasted. If a problem has been solved but not golfed, it can still make an interesting golf question. If a problem has been golfed elsewhere but not optimised, it may make an interesting code challenge. If the question adds a non-trivial extra challenge or new perspective I welcome it.
Identical is boring
I agree that asking the same question with no changes is boring. Even if you take the approach of tackling the question without looking at the known answers, it's not as fun to compete against people knowing some of them will be basing their answers on existing research.
Know the difference
What I would be wary of is genuinely new questions being closed hastily because they appear to have known solutions. This could be a problem where the difference is subtle but rules out existing known solutions. Also a question that genuinely is already solved could be tweaked to be more interesting, so could still make a good question eventually. In either case I would encourage comments to let the question poster know that clarification would help.
I'd be inclined to close vote if there's any doubt what the question poster intended, to make sure any required changes are made before answers come in. However if it's already clear that the intention is to post a solved problem, then I wouldn't close vote as it isn't an on-site duplicate, even if it is clearly an off-site duplicate.
I would be happy to reject such off-site duplicates if we had a change to our guidelines, but under current guidelines I don't see them as something to close, just something boring to consider down voting.