You can’t really refuse their business if they want you to be on the app. They will just add you and direct the driver to pay with the issued card like any other customer. The consumer still sees it as “you accept DoorDash orders” though. Then the sales pressure starts since they have your customers.
What pressure? They are going to threaten to delist you? Disappointing their own customers in the process?
The usual marketplace tactics. Dashpass and promotional feautes, search rankings, etc. Well documented.