Yes, many potential duplicates of this:
What to do with cross-site duplicates?
Is cross-posting a question on multiple Stack Exchange sites permitted if the question is on-topic for each site?
Can I ask the same question on more than one Stack Exchange site?
My suggestion differs. It is to let users choose which sites should their question appear on (and rather then having to copy-paste it to another site).
Yes, I read all the arguments that a question belongs on one site and is off-topic on all others. But this highly upvoted question: When will Stack Overflow become irrelevant? and its answers make it clear that this is not exactly the case. Even if we assume that sites are completely non-overlapping in their topics, they are overlapping in terms of people who can answer questions.
I can answer questions on programming. So I should look in both programmers.stackexchange.com and stackoverflow. And if I were a game developer I would need to look at a third site. Well, I don't - I only browse stackoverflow. So my potentially useful answers will not be seen on programmers.stackexchange.com. You may say that this is a choice of every user, but I want to answer programming questions. Why should I look into 3 sites?
You see, this is all from the answerer point of view. But these are the people that drive the sites.
The idea is for the question posters to choose which sites their question they want to appear on. If I have a question about my ubuntu, right now I have no idea whether I have to ask it on linux, unix or ask ubuntu. Or super user, or server fault. I have to read all 5 sites' descriptions. And that's not very asker-friendly. You can even suggest sites that are a possible match (like suggesting duplicates).
I think there is an overdiversification of topics. This is not necessarily bad per se, but it might need some extra features (like the one suggested) for a greater benefit.
(Note that I don't tag feature-request, because I didn't define the feature details. It might be showing questions on multiple sites but having the question actually reside on only one (in terms of UI), or having the question synchronized between multiple sites)