In the late 90's I worked for an online mortgage broker, and 9 times out of 10 when we ordered an appraisal, the appraiser would ask us what the selling price was and return an identical figure for their estimate.
We ended up just guessing high and lowering our price a couple of times until someone bit.
The appraiser just needs to make sure that the number isn't fraudulent or crazy.
For the most part, the banks and brokers re-sell those loans immediately, so they don't stay on their books. All they need to protect them from lawsuits later is proof that they followed the process to the letter -- which involves getting a written appraisal.
No mortgage broker or Realtor ever got rich by picking a fight with the appraiser to lower the appraised value ... there is literally nobody present at the table who has an incentive to push the value down.
But it's been a decade now since the housing bubble revealed that appraisals are meaningless.
Why has no one eliminated them?
Whether those efforts were successful or not is another discussion.
If the bank won't write a loan for the agreed price, the original contract is void, since it's contingent on loan approval. If the seller's heart is set on moving, he might well lower the price.