My issue would be when buying a car. What if you can't access the internet, you'll have to ring them up and wait around for ages to buy tax. If it's a weekend or out of office hours you can't drive the car.
To get a full refund you'd have to sorn the car at the end of the month before you sell it, then the punter can't take the car for a test drive, you can't use it at all. Who is going to do that? The DVLA will make millions from middle of the month refunds.