There's a very similar scheme at Canary Wharf. When you collect your ticket at the barrier on the way in, you'll find your ticket has your number plate printed on it.

It's still paper-based and you pay at a machine* but when you leave, a camera at the exit barrier recognises your number plate as having been paid, so it's much quicker than faffing (that word again) about, trying to find the ticket down the side of the driver's seat and then stuff it in the machine.

Point being, we have the technology.

* It's a while since I've been there but I think, at weekends, you can get your ticket validated in any shop where you spend over ten quid, to get two or three hours' free parking.