On my OS (Ubuntu Linux) the OS prevents writing to files that are already open for writing,

That's a very odd Unix. One I've never encountered before.

Now, there are some OSses that won't allow you to write to pages binaries currently being executed by some process (giving you a 'text busy' message), but that's something else entirely.

(The same is shown by trying to open the same file twice using "vi".)

Ah, yes, that editor. The one that tries to be vi but isn't. I'm a vi-lover and have been using vi and vi-clones for 25+ years. But I loathe environments where 'vi file' starts up an editor that isn't quite 'vi'. By all means, if you call it 'vi', then have it act like 'vi'. If it acts otherwise, call it otherwise.

As for that editor, that editor creates another file in the same directory, and if that file exists, it thinks the file is already edited and starts complaining. That has nothing to do with the OS - that's just a behavioural thing of the editor that isn't quite vi. Using another program, I can happily modify the same file.