It’s a sad state of affairs when a malfunctioning doorbell can prevent cars from starting. The button won’t open the door, whatever, just put the key in the lock and try not to strain yourself, but when the car has to be physically towed out of proximity?
Technology will always fail, there has to be redundancy.
There is redundancy. In the “key proximity” systems I’ve seen (Audi and BMW), there is a spot where you can put the key in case the usual key detection doesn’t work. The car will even tell you to put it there if it can’t detect the key. It’s supposed to work with empty batteries in the key, so it’s probably using something like NFC rather than 434 MHz radio.