The way I read it is that costs are unbounded, not profits are unbounded.
The health insurers are responsible for negotiating, checking and denying costs. If not them, you would have a state bureaucrat in charge of denying claims. Many will argue this is better, but it still isn't a blank check.
As you point out, health insurance companies make money as a percentage of bills approved, not bills denied. The vast majority of Americans don't understand this.
The completely different and more insidious problem is that this provides an incentive to approve claims, but drive their prices up, like any government regulated cost plus contractor.
Cost Plus contracting only works when there is a competitive market and high transparency.
Government laws tying healthcare to employers mean there is almost no competition, and healthcare costs are inherently opaque due to their complexity.
