I don't ignore the possibility. I just disagree with the idea that the AMCs have no incentive to shop fees if their end is fixed. I think they're under constant pressure from the lenders.
You seem to be banking a lot on the point that the bundled fee is labeled "appraisal fee" and should therefore only go to the appraiser doing the work. Even though the "label" play is clearly not how it works when the appraiser is working on staff or in a fee shop or for the govt.
How to address this: 1) AMCs should not be in the fee business with appraisers. The right way to do it would be for the lender to tell the AMC the cost for the AMC service to them, just like every other customer pays for a service. The appraisal fee the lender collects from the borrower covers the appraiser's fee. The AMC can do all the rest: the admin, review, order, deliver, and review. If the lender can pass on that AMC cost to the borrower, then they could do so.
2) Being that it is not teh system we have now, the AMC;s shop fees are typically not fixed ( though if a lender isn't on it, then it would be ). The AMC's that use a cost plus system are typically an AMC owned by the lender for their own order processing - it is owned under a different name under a different division ot the lender.
3) The independent (not owned by the lender whose work they process) an independent AMC does shop for fees, because their livelihood comes from teh split of the appraiser's fee that a borrower paid -. They act like a wholesaler or middleman, but one that has a very odd place compared to other businesses since GSE appraisals are the only area where the ordering of an appraisal is restricted ( the loan officer or loan broker as an individual is not allowed to select the appraiser ) .
The bundled fee on the HUD is only allowed to be split between a third party and the appraiser. It does not deal with fee shops or govt agencies. That is why a lender can not split fees. That is why a lender to be in the fee-splitting position, forms a separate division AMC to be a third party and only then can it legally split a bundled HUD fee .
An employer such as a govt or fee shop does not split a fee. - because they are not a third party. The fee shop or govt agency acts like an employer -and produces the appraisal and pays the appraisal if it uses one for the appraisal at whatever rate they decide. The AMC is a thrid party middleman service. IF an AMC hires an appraiser for staff then it is also an employer..
As far as constant pressure for the lenders, I do not see AMC's under pressure from lenders to pay the appraiser less. The lender gets nothing when that happens. The lender passes the borrower payment along to the AMC, whether the AMC splits it 80/20 with the appraiser or 50/50. The lender gets no $ either way ( unless a kickback scheme is there, which I can not speculate on ). The lender pressures the AMC for turn time /quality and delivers the appraisal for the $ amount the borrower paid as the through payment, so the lender is not charged an additional cost. Why would a lender pressure an AMC to pay an appraiser this or that amount on each order? Or be involved in each fee bid ? What a PITA that would be, since the lender hires the AMC to separate themselves from the appraisal process.