I want to post what I've found out... which isn't much. It seems that maybe the way it works is that managed-type plans, like HMO's, PPO's, etc., have pre-arranged prices by contract. So even before the deductible is met, the price has already been fixed, despite whatever the doctor/hospital may bill. I think it only works this way for in-network doctors/hospitals. Out of network, I think it becomes a battle between the insurer and doctor/hospital. But surely, the insurance company will not care to fight for good pricing very much before the deductible is met.
I think that with indemnity plans, it is like always being out of network. So only a very small incentive for the insurer to fight for low pricing for you until the deductible is met. And especially so if you have a high deductible.
I may be completely wrong, but it has been hard to find knowledgeable (and impartial!) information about this.
I think I'm probably going to go with a high deductible, PPO, HSA type plan.
And thank you for your help, Rooted. I laughed when you wrote "reasonable cost," because that must mean that the doctor/hospital charges an "unreasonable cost" by default.