This was supposed to be the benefit of HMOs. There would be single-pricing, and all carriers are aware of this pricing beforehand.
What I think we need, however, is a model that doesn't depend on single-pricing to work, because the real world isn't single-buyer.
People tried to solve it by creating healthcare savings accounts, but the solution itself is very complex, and the end user is often in situations where they don't have the ability to negotiate (e.g. emergency health care). So in practice, the financial benefits seem to accrue with low-care patients, not low-cost-of-service patients, meaning it doesn't affect the system in the right way.
Ultimately, I think the only way to fix it is to start adding negative pricing pressure in small ways to the system, not trying to tackle the whole problem at once.
For example, waive deductibles for treatments which are billed below average (mean? median? in any case, this has to be independent of list price). That creates a financial incentive for insured patients to both seek out billing information, and to lower it.
What's great about that (for insurers) is that you're specifically altering behavior of your most cost-conscious customers, who tend to be your lowest margin customers, without mucking about with the profit margins on your most valuable customers.