I think you're mixing up a few things here. The co-pays are meant to make the patient directly pay some of the cost to decrease abuse of the system. There are many different structures for co-pays so saying anything general is kind of difficult, but there are reasonable arguments supporting such a system. In Sweden for example you do have to pay certain costs (which are capped) for essentially the same reason.
But that has nothing to do with the fact that prices vary so widely for the same products and services. Personally I think that the US system should at a minimum require that
1. All medical products' and services' costs to published publically;
2. All costs to be non-discriminatory (meaning everyone regardless of any insurance plan or none must pay the same);
3. All costs be available prior to any services provided.
In other words, there are no negotiated plans with different prices, there are no surprise bills, patients actually are able to understand costs, and real competition is actually theoretically possible. None of this would necessarily preclude an insurance plan from having co-pays, it would just make the only point of the insurance plan purely financial and open as it should be.
Of course the US could just move to a single-payer government-run system, but that's a different discussion. If the goal truly is to have a market-based system, then I think my points above should be implemented.