We've tried something pretty much like that.
Specifically, both Writing Codidact and Scientific Speculation Codidact were seeded with content from Writing SE and Worldbuilding SE, respectively. (The former with what essentially amounted to a full copy; the latter with a subset of posts.)
It sounds good in theory, and I was actually in favor of it at first, but it does have one huge drawback that has become obvious to me in retrospect.
It makes the new site basically indistinguishable from the old one at the time of the import.
It thus gets difficult to answer the obvious question of "why should I go to X Codidact, instead of X SE, which is where everyone else is actually, you know, adding new content?". The Codidact site simply lacks any kind of a unique selling point other than the fact that it isn't Stack Exchange. Which is a major point for many SE refugees, but let's face it, for most people it doesn't really matter which entity is hosting the content.
Thus, without a reasonably large user base who are basically just waiting for the new site to pop up before they post additional content (questions and answers alike), differentiating the Codidact site from the corresponding SE site becomes very difficult. It then makes more sense to do something similar to what the folks behind the Electrical Engineering Codidact did: have a plan for seeding the new site with some content, and then draw in subject matter experts who can both answer questions that get posted and help spread the word.
Now, if a SE site is in actual danger of being shut down and the community wants to preserve the content in an easily browsable form, or maybe even set up a new community elsewhere and migrate the content, that's a different matter. However, a discussion would still be needed on the reason why the site in question is in danger of being shut down. The reason why Stack Exchange might want to shut down a site might not apply to a Codidact site, but without a frank discussion about the specific case, it would be difficult to know.