When I worked in AMCland, the great majority of lenders we worked with wanted a fixed price, or at least a fixed price per state. And, who could blame them? Under current disclosure rules, if a lender's GFE indicates the appraisal cost will be $X, and it turns out to be $50 higher, then the lender has to provide new disclosures, and no one wants to do that.
For example, suppose the agreed upon fee in a state is $650, with no change unless the appraiser fee exceeds $1,000 (a very typical arrangement). If appraiser charges $500, the AMC grosses $150. If appraiser charges $650, then the AMC grosses $0. If appraiser charges $750, then the AMC, eats $100. If appraiser charges $250, then the AMC grosses $500. All of those scenarios can and do happen.
If one wants to change how lenders approach AMC fees, then the key change would be to allow changes in appraisal fees without re-disclosure. Unless or until that happens, the fixed-total-price model will be the one that most lenders will seek.