I'm using NixOS where every version of every dependency of every program I install will be saved until I cleanup the garbage (1 command) so I don't have your issue.
If this was Windows you wouldn't be able to update Firefox while it was running because Windows doesn't support overwriting open files (technically you can rename them and insert new ones with the same name, but that's not the point).
You're holding it wrong and blaming the project, close the software you update before you update and you might have more success.