I think you need to decide what it is you want. On the one hand you say you want a free market, yet then you post that appraisers should not have to compete on price, which is a hallmark of a free market.

Which is it?
Since the specific topic is Regulated mortgage lending, where due to prohibitions against a borrower or a loan officer selecting an appraiser, it is not possible to have a free market for appraisers - so asking me what I want is a straw argument.
What I want is to remove the huge market share advantage that exists now for the AMC's via the bundled fee, where the AMC does not have to charge a cost to the lender for their AMC service, be scrapped.Or the AMC fee percent is capped since the system has been exploited beyond the normal % management charges talent, usually in 15% range. If a lender wants to pay an AMC more than that cap, they can.
When I reference the free market system, I am doing it to compare the usurious fees AMC's now enjoy at the appraiser's expense under the current system. Can you honestly tell me taht the AMC could charge, and get, $200-$400 per appraisal order if a lender had to pay the cost ?
What do you think a lender would pay if the lender had to pay the cost of AMC services ( as a hypothetical)
I bet an AMC would be hard-pressed to get $75 an order if a lender had to pay for it , and many lenders would not use an AMC and would return to their own panel management.
Whereas appraisers can and do get paid $500-$650 ( avg ) for mortgage res loan work when no AMC is involved, and for residential private order work, and for residential work from attorneys, estate planners, RE agents, or others. And can and do get more $ with litigation/specialized/complex/high value /rural or in areas where geo location sees it occur.