Sure, but they can say, this is the shop we will pay ourselves, or you can go somewhere else and we'll cut you a check. If you need the repairs done faster than they cut checks and don't have cash on hand, it's a strong incentive.
Which is why people should have savings and learn some life skills like basic auto repair. Body work and paint I can't do myself, but that's mostly cosmetic (look at the number of beat shitboxes rolling around in the US). But you should be able to get a car into running order or acquire a rental vehicle while you wait for the check. Rental vehicles are usually at preferred rates when associated to an insurer and depending on the policy are covered.