With over 50 years experience in hospitality and 25 of them currently offering POS products and IT services for the hospitality industry I can offer that there are ongoing performance and timing issues, charges for orders that weren’t completed by customers, poor reviews for delivered food, tampering and the costs involved with delivery. Then there is the mostly non discussed issue of who owns and keeps the customer info and if and how it’s used to promote your competitors or steer your customers.  If your in the prepared food business and can pass off up to a third of the sale price of your product and your customer information in the hopes of gaining a new patron then perhaps third party delivery is the option versus the in-house cost of delivery. 
Delivery is a serious commitment of resources and planning from menu items that can hold for the pickup and delivery time, correct containers for each item, presentation of the item in its container, sealed tamper proof delivery containers and correctness of the order, extras and service ware at pickup, etc. and then how to handle and prepare timely delivery orders with a full dining room and twenty orders on the string for the hot line?  
Delivery is the hot button being promoted, not surprisingly by third party delivery providers, as a means to maintain volume while the prepared food market gets more and more overcrowded and justified by delivery statistics from Amazon, pizza, subs, wings and oriental grub in paper bucket providers that are the most trucked about delivery offerings.  If your product, pricing and image doesn’t fall into this accepted style of receiving an order then you need to carefully review how your brand and operation will be effected by offering an a la cart delivery menu and service.