Had two Audi’s and on both occasions we paid the AP a couple of days before collection, BUT on both occasions they were stock cars and we picked them up one week after ordering. Also we had a journey to both dealerships and wanted to remove the risk of a problem with payment on the day of pick up (I know of someone who drove over 100 miles to collect a car and their bank blocked the card payment and because they kept trying it then blocked their card completely).
We are not dealing with some kind of crooked third party and to have a quick, smooth pick up I would pay in advance every time. However as stated in other posts this is not necessarily a requirement.