But wouldn't it make more sense to use the Win key for it than Alt? I think copy/paste could fit into the OS/DE layer.

Maybe. It's borderline text-editing (the majority of usages are text, and probably within the same application).

Also if we consider, how it's implemented: the app is responsible for content-type negotiation, if I copy a file in my file manager, it's the file manager's responsibility to yield file contents of I paste to another file manager, and yield the file:// uri if I paste to a text editor. So also border-line app functionality...

As I said, I don't see an obvious solution, and even if I had full freedom to design everything from scratch, I don't know which option I'd pick.