> On Windows, Firefox can't be updated while it's running because the files that comprise it are locked by the running application.

I don't know how the "behind the scenes" work but you can run an update while Firefox is running. We do it all the time. We push security updates to our clients via an agent. It runs the official installer in silent mode. It is like OP described: You can't open new tabs (ok you can but they will not work) until you restart the browser, but the existing tabs keep working.