Doubtful that someone running an old unsupported OS is keeping their browser up-to-date
It is really doubtful that someone running an old unsupported OS is keeping their browser up-to-date.
The browser isn't going to fix the security holes in the OS and hardware.
Mozilla will have statistics on what OSs it's latest browser versions have been installed on. Are any of the last 3 versions running on XP and Vista? Yeah right, none. I couldn't imagine otherwise.
If people are content to run their old computers on unsupported old software, the web browser will be just another piece of old unsupported software. They can keep running the old versions.
Don't make life more complicated that it actually is.