The "solution" to this, in the run up to the '08 crisis, was for appraisers to "help out" by fudging their figure to make it match the sale price. I know this because a real estate agent whose husband was a loan officer, told me so. "I know they were just trying to help out with these new regulations, but it's had the unintended consequence that appraisers can't fudge their numbers slightly higher to match an offer that's only a couple percent above the natural appraisal, like they used to". LOL, yeah, the exact thing they were trying to accomplish was an "unintended consequence". Talk about not being able to understand something because your paycheck depends on it.
Possibly some appraisers in at least some markets have figured out ways around this, and are back to fudging numbers. I dunno.
My appraiser (on a refi) was walking around the house with me and basically asked what I thought the place was worth. That was what it appraised for. (The contract price on an original sale has the same property: what the buyer thought it was worth.)
Ideally those are tethered, but the appraisals didn’t give me a great sense of independence.