Mastodon moves also take your following with you. You’ll still have to reimport followers, but you don’t lose your ““audience””.
There are software out there (Sharkey for microblogging (Firefish also had it but theirs was broken and leaked DMs), PixelFed for images from Instagram specifically) that allow some form of post imports, but these are only brand new posts that happen to have the same content as the old ones, and not “replacing the author of a post”.
There are work going on regarding nomadic identity and more seamless account migrations across instances, but hell will freeze over before any of the mainstream fedi software implement anything close to that, mainly due to how significant of a conceptual change that is.