Flutter can be socialized for mobile OR desktop OR web. Having all three in a codebase requires lots of code and alternative layouts to properly handle each platform. It's not a "one size fits all" solution, actually to the absolute contrary it's a solution that you have to tailor to the UI you want to build.

I'm making desktop apps with Flutter (it's awesome) and my apps can't ever possibly hope to run on mobile. I'd have to remake most of the damn thing in order to make layouts for mobile.