Lenders and other institutions who frequently order appraisals are familiar with something called "Appraiser Independence". They understand it is unlawful to directly or indirectly coerce, instruct, bribe or intimidate a person who provides valuations based on anything other than their independent judgement including the withholding of payment because you wanted a different value opinion.
That being said, frequently appraisals are needed by private citizens for reasons such as listing a property, for a divorce settlement, for diminished value claims, for estate planning, for estate tax purposes (i.e. date of death valuations for tax purposes), etc.
Personally, I have worked with many appraisers over the years. Most of my peers simply will NOT do business directly with the general public based on their past experiences. If they do, they will insist on payment up front before even inspecting a property or delivering an opinion of value.
Why? Well let's take the case of a divorce, for example. Rarely are the parties involved on great terms. If they could agree on 'stuff' they probably wouldn't be getting a divorce. It is usually the case that one party is wanting an inflated value (the spouse being 'bought out') and the other party is wanting a deflated price (the spouse who has to buy them out). This can frequently result in both parties being upset with the appraiser who likely gave them a very accurate value opinion.
Another example is when heirs to an estate need to establish a new cost basis (as of the date of death) for a property. They may likely be looking at selling a property soon, and are hoping to minimize their capital gains. None of us like to pay taxes, but most appraisers are not willing to risk their license which required thousands of hours of training and experience just so you can have an inflated value to give you a better 'tax break'.
In fact, most appraisers are so analytical, they couldn't figure out how to fake an analysis to give you a fake number if they tried --- and we aren't going to try! Keep in mind, any appraiser worth their salt will gladly consider any additional valid data you provide but arguing that a website says my property is worth X and you said it's worth Y isn't a valid reason.
You don't go to your doctor and tell how to perform your surgery. And if you don't like their diagnosis, they are still sending you a bill. Do you tell your plumber how to install your water heater or insist they do it the way you saw the 'do it yourself' guy on You Tube do it? Do your tell your grandma how to make her mom's mac and cheese recipe?
Bottom line, the public frequently needs to behave more professionally when hiring appraisers. We serve a function for the public trust. We are supposed to provide an independent unbiased opinion, and no matter how much we like you or even no matter how much we dislike you, our opinion cannot and should not be influenced. In this case 'We are the expert".