Wouldn't putting an electronic key inside a small Faraday cage render it completely useless?
The idea of that case is to protect the keys while you're sleeping. You need to take the keys out when you want to use them to drive the car.

The main problem is trying to cope with key-relay car theft. This tends to happen at night, with thieves making use of the fact most people keep their keys near the front door. So the key signal just needs to be relayed from just the other side of the wall (where the key's signal just about reaches), to the car. Then the car can then be unlocked, started and driven away. The idea of the case, is you put the key in the case, a lot less RF gets out, so the signal is so low that it cannot be relayed to steal your car.

Then you'll need to take the key out of the case in order to get in your car. So your key-less entry and start isn't quite as easy as it would otherwise be. So yes, the keys are out of the case then, but you are in a position to see/use the car, so that should stop anyone stealing your car.

Alternative solution to this is my prefer ed one: keep keys further away from the door.