Re: "...can pick up the signal from keys..."
"...so that when the key fob signal fades away, the car explicitly counts down to engine off. ... Wouldn't it already do that?"
Our Ford doesn't. As long as the key is in the car when you start the engine all is fine. It is then perfectly possible to get out of the car leaving the engine running, take the keys with you into the house to get some forgotten item and put the keys down and forget to return them to the car with you. I image that it would then be possible to drive off without the key. I haven't tried it but with my luck it won't be long until I do
They don't switch off in case some idiot has thrown the key out of the window.