nobody actually pays those bills. They're just some elaborate dance between insurance companies and hospitals.

Sometimes there is an elaborate dance between the two on pricing. Sometimes the insurance company dances on its own to determine why the service is not covered.

If you don't have insurance, the cost is lower

Depends what you mean by cost. insurance is always out to make money, that means paying less, and negotiating lower prices with providers. However, there are some situations where it benefits both the service provider and the insurance provider to inflate the initial price, and negotiate a steep “discount” to a final price (a portion of which the patient pays) that is higher than the non-insurance price. But I don’t remember the exact details, and I may be conflating this with some other healthcare industry scheme.

or removed entirely. Supposedly.

If a hospital is nonprofit, I believe they are required to have a (self determined) charity care policy that they must follow. If you make below a certain amount, you can apply for relief, but that also applies for to after-insurance costs, not just no-insurance costs. For-profit hospitals will rake you over the coals and send collections after you. Part of the problem with charity care, is that you may have to ask for it, and few people know enough about it to do so. And you may have to ask for it in the right way. If you aren’t specific enough, they may offer you “financial assistance” which is just a payment plan. Then they’ll treat you the same as a for-profit hospital would.

If you’re interested in a deeper dive, the Arm and a Leg podcast is a great show about healthcare costs in the US.