lender quotes the borrower a fee and then can not deviate it
I don't think that is exactly correct.
Correct me if wrong, but I believe D-F allows a 10% tolerance on the GFE. With the " average total closing costs in this analysis ($8,686) represent about 8 percent of the mean loan amount. Obviously, closing costs are a significant expense for borrowers and are worthy of attention and scrutiny. But another important issue—one that was beyond the scope of this analysis—is whether the disclosure process provides information in a timely way so borrowers can actually use it. A borrower who finds out on the day of the loan closing that settlement costs are greater than estimated may be in a difficult position. If the loan is necessary to purchase a home or, in the case of a cash-out refinance, to gain access to needed funds, the borrower may be unwilling to back out of a standing loan offer. In the rush to settle the loan, borrowers may not even recognize cost increases. In future analyses of the disclosure process, the matter of timing warrants careful assessment." (Minn. FED)
So, on an $8,686 closing, they have $868 margin and since most costs will be fixed, only the variable ones (like the appraisal) impact the Good Faith Estimate. I don't believe that GFE implies a line item 10% but rather the total closing costs. Obviously, a badly under-estimated GFE may require the lender to pay the difference. The problem for lenders is thinking it is a SFR and not doing the 'due diligence' to find out before offering the GFE what the fee will be. This should be a sign to bankers they need to order an appraisal early in the process so they can modify the GFE early. For instance, the house might be lake front, or might have an ADU, second home, large shop, etc. What appraiser doesn't want an additional fee for additional work?
Lenders need to be transparent to the borrower. They also need to be transparent to the appraiser. I've been sent to do "SFR" appraisals on 2 commercial dog kennels, and a new house with a commercial cabinet making shop on the same site. It's frustrating. The last dog kennel wasn't finished (new construction as well) for well over a year, after I had asked to be taken off their vendor list for similar antics. They begged me to do the final inspection, and I refused. Internally, their policy was to use the original appraiser for finals, but I bet they sent one of their own appraisers out to do that rather than another roster appraiser.
So, send me the assignment and I will look it up, and report back. If you ask me what's the fee, I will give you my good faith estimate and stick to it. But with the community banks I use, I think they simply over-estimate the appraisal fee and closing costs are generally lower than the GFE. The Minneapolis FED said that 61% of GFEs are higher than the actual closing costs on the HUD-1.