Theoretically because you are not the sole provider offering that service and the patient could go elsewhere, or in this case, the insurance company would require the patient to go elsewhere. Obviously, this sucks absolute donkey balls and health care will always involve a healthy dose of "I can't just shop around for where to get help for a heart attack".
In my naive opinion banning discriminatory pricing (no special negotiated insurance pricing), the sale of medical debt, and counting bill forgiveness as tax deductible charity would be a good start. With the absolute technical and capital-intensive marvel that is modern health care I just don't see anyone being able to reasonably get away with no insurance. Maybe there is a mandated co-insurance for all plans that could be covered by HSA accounts that everyone would get access to. That way there is a cost that is transparent to the patient that scales. At that point though I would just go to single payer.
(Rant incoming) Another thing that might need to happen is billing caps based off of certain outcomes. Especially in the emergency medicine realm. If you go to the emergency room and rack up a huge bill for something simple there should be a cap on the amount the hospital can actually recover. All I see is (rightfully) constant bitching and moaning from ER staff that people should be going to primary care or urgent care for issues which are less resource intensive and cheaper. The issue is the ER could provide those same services for just as cheap. Build out those same capabilities in or near the ER. The triage nurse can then send those low priority patients to the facility right down the hall. The issue is hospital admins have no incentive to do that, because as you said, why bill $200 when you can bill a minimum of $2,000 when you have your patient captive.
I also think it is silly we ask people to self-triage. It externalizes a lot of the costs to other parts of society. I can attest to this from the constant Volunteer Fire Department air-raid sirens I hear followed by a "EMS to Well Now Urgent Care for Patient in Distress". I'm sure the volleys love having their evening interrupted when it could have been a simple walk down an aisle.