The problem with waiting isn't with the system, it's with the way it's implemented in the shop. Many shops in the UK will accept a card payment in literally 2 seconds, therefore Apple Pay takes the same amount of time. The first shops that spring to mind with this are McDonalds and Asda (Walmart).
In some smaller shops the system is different and you can easily be waiting 30 seconds upwards for the payment to be approved. The only way this is different with Apple Pay is that you only have to hold the phone for a moment to pay whereas a card has to be in the machine the whole time, you'll still be stood there waiting the full amount of time for the payment to be approved. Strangely Subway is an absolute nightmare for this, for such a large chain of stores their card system is dreadfully slow but there are much slower ones out there.
In some smaller shops the system is different and you can easily be waiting 30 seconds upwards for the payment to be approved. The only way this is different with Apple Pay is that you only have to hold the phone for a moment to pay whereas a card has to be in the machine the whole time, you'll still be stood there waiting the full amount of time for the payment to be approved. Strangely Subway is an absolute nightmare for this, for such a large chain of stores their card system is dreadfully slow but there are much slower ones out there.