This Freakonomics-style argument doesn't work. The only price that matters is the market clearing price. Appraisers don't know that more than anybody else. The only thing an independent appraiser would do is use (well-known) comps to anchor the price, which is not something a seller wants. Rather, a seller wants competition among buyers.
I used to think that real estate agents were a waste of time until I lived through several difficult transactions. Each real estate transaction involves negotiations for loans, inspection objections, and various legal details. For example, a good real estate agent will make sure the title commitment documents are in hand early enough that you have time to review them, because they often have a lot of mistakes. This can kill a closing and/or require post-transaction work to correct.
I bought a house in the middle of a flood (Boulder 2013). The inspection objection had already been negotiated before the flood occurred. Getting the deal done was a huge task, because the seller was lying about the house being affected by the flood. I still wanted the house, but I needed proper compensation for the remediation. My real estate agent did an amazing job of bringing the deal together by tossing in some money and getting the other broker and seller to contribute a bit.
I'm now living with the above real estate agent, and she's on the phone right now at 7:45p working on a deal. I have watched her pull together deals, and the important thing is that all her clients are happy. I have met many of them, and they are very grateful for her work. I know there are many other agents out there like her (maybe not quite as good :-).