From what I've heard, there's no trade off between reliability and cost. The cheaper vehicles will probably be the more reliable ones as well, due to learning effects from increased launch frequency.
I agree with your first statement. The more launches SpaceX does execute the more they can learn from it to reduce cost.
What I think was going on with NASA was overengineering parts for a ride with over a 1% loss rate. One can spend a lot of money making a nearly perfect part or process more nearly perfect. But if the overall system is unreliable and remains unchanged despite the improvement, then that expenditure is effectively wasted.
Actually the first reason (I don't disagree with you) why the cost was never reduced is that NASA's engineer was never given an incentive nor an opportunity to redesign to incorporate all the lessons learned to BE MORE EFFICIENT. As a result we are left with outdated equipment with limited amount of spare parts. We are forced to make modifications on an outdated equipment to make it "safer" when we could have done the same thing by building/designing a new crew vehicle. In another words the lack of refresh/upgrade cycle is what bite NASA in the end, and mostly because of political reason.