Also, in the vertical model, the profit is shared with two parties -- the restaurant and delivery agent. In the horizontal model, there is an extra party which needs to be paid -- Postmate/Uber/DoorDash/etc. Presumably, the app experience makes it worth to pay more for the delivery, to pay this third party, but that has not yet been the case.

Also, once one party owns the relationship (e.g., the app), they can try and take more and more from the other parties while putting more burden/risk on the other parties.