When I was in AMCland we took a different approach. When an appraiser set up their profile part of that was entering their base fees. When an order was assigned, the fee offered initially was the base fee set by the appraiser. The fee could be changed if the property was complex.
We also had an objective way to score all appraisal reports. We created codes for every reason a report could be sent back for revision, and each code has points associated with it, with higher points for major errors and lower points for small things (e.g. 1 point deduction for a typo in the zip code). If a report could be sent to the lender with no revisions at all, it got 100 points. So, a report with just a typo in the zip code would get a 99. We could compare the scores and predict how much QC work would need to be done, and 2/3 of the assignment logic was based on the quality score. The other 1/3 was based on turn time.
An appraiser could set their fee at $100, but they still wouldn't get any work if there were available appraisers with higher scores. I know some resent having their work scored, but without some sort of ranking system there is no way to get work to the higher performing appraisers.
When we were audited by lenders they would often ask us to show how we picked an appraiser for a specific assignment, and we would have to go through all the scores for the available appraisers and show that we did not just pick the appraiser with the lowest fee. Even if the lenders did not audit, we would never have just picked the lowest fee because QC rejections cost money. On most orders, if we rejected a report more than twice, we were basically eating the profit. There was high motivation to assign to appraisers with high quality scores.
Bidding was only done for very complex and/or high end properties. I have long said that I do not know how any AMC assigning based solely on the lowest bid can claim compliance.