this is true, and we add on beer and wine for the customer as well. I managed all deliveries and phones for a pizza shop here and as chinese shop and it worked well because they put delivery second to dine-in, so customers had to wait for delivery. In my resort town in the winter its just nuts with the restaurants so deliveries are always well over an hour, buys me time.
I think though for a new pizza shop who is starting out a multiple restaurant delivery service (RDS) would be a benefit for them. The RDS publishes a menu for them (gets the name out there for the new pizza shop) so free advertising and most people know to call the pizza shop as they either charge cheaper for delivery or the delivery is free. The RDS only pushes delivery for the rest to generate their own deliveries, unless a deal is made. When some of the pizza shops here are slammed they sometimes call me to come in and grab a few orders for them and i charge a flat fee (6 to 8 bucks) as opposed to the sales commission i get when i call in my own orders. Beleive it or not about 40% of my overall business is pizza sales and my customers pay the $6.50 delivery charge without hesitation and if they add on beer or wine, they pay $13.00 for delivery. I even got locals trained to call me for pizza and they pay our VIP delivery of $5.50, they know I have more drivers on and i’m faster and more reliable.