I suppose a better question then is, why isn't this routinely done for factory firmware? It seems that such a distro would be immensely helpful for any kind of recovery. Not to mention that, if it has a web browser, it could be used in a pinch to get stuff done even on a machine with a failed SSD etc.
Lenovo has some form of what appears to be Linux on their newest laptops that can do internet based recovery of the OS. I haven't had time to play with it. It's been way too long coming - Apple devices can boot into a lightweight MacOS and do this and have been able to forever.