When you're at 30,000 feet, nobody wants to go experimenting with a system controlling critical flight operations that has gone into an unknown state.
The pilot often has the option of rebooting the system and trying it again, but that's dangerous. On an episode of "Aviation Disasters", I don't remember the exact details, but the pilot got a warning of a failed system. After a consult with the ground, they told him to reboot it. After a while, it failed again. They told him don't worry about it, reboot it again.
It (the airplane, that is) crashed.
Aircraft systems are designed to be decoupled from each other as much as possible, so failures do not propagate. In particular, they must not propagate to the backup system, or the "safe mode". The engineers do work hard at this, and sometimes they don't get it right, and another bitter lesson is learned.
The "safe mode" system must be physically and electrically decoupled from the normal system.
An example of getting it wrong is I've seen demonstrations on TV of people hacking in through the wireless key locks on a car to take control of the brakes. That's seriously bad engineering - not so much the vulnerability to hacking because happens, but the fact that the door lock system is connected to the brake system. It's cowboy engineering at its worst.