Currently, closed questions are still indexed by search engines. This makes sense for duplicates, but I think this is counterproductive for other closed questions.

Encountering a closed question when search for something gives a bad first impression to the user, the closed question often won't be helpful to the user as it might not have gotten an answer before closing and was likely a bad question anyway.

Getting anonymous visitors also won't help the asker to get his question reopened, as visitors from search engines are unlikely to have the required 3k reputation.

One counter argument would be that closed questions should be deleted anyway after a while. And while this is true, in practice this doesn't happen systematically and many closed questions are just left alone and forgotten. There are 128,000 undeleted non-duplicate closed questions on Stack Overflow, so clearly the deletion of closed questions isn't happening effectively.

Indexing bad questions isn't making the internet a better place, it arguably even makes it worse and we should stop doing that.

Jeff Atwood seems to agree with me, at least for closed questions without answers:

Yeah closed and unanswered should definitely be delisted. These kinds of questions usually have negative votes so they do have a lower score in the sitemap weight but I am not sure how much emphasis G gives that. I will forward this on for SE to think about improving.