You seem to have missed the point of the appraiser.
The market clearing price is not set in stone. It is determined partly by the actions of the agents.
The appraiser's estimate of the market clearing price would set a measuring point from which the agent's performance can be measured. Agents are then paid according to how their performance exceeds the expectation.
Without the appraiser's estimate, the performance of the agents can not be measured. There is no way to reward good performance or punish bad performance. The agents are simply collecting their cut of the transaction.
In this case, bad measurements are OK. They average out over time. If the bias is one way, then one type of agent (seller or buyer) gets a bit more pay than the other, but this is not a disaster and is compensated by agents competing to work on the higher-paying side of the transactions.
The market clearing price is not set in stone. It is determined partly by the actions of the agents.
The appraiser's estimate of the market clearing price would set a measuring point from which the agent's performance can be measured. Agents are then paid according to how their performance exceeds the expectation.
Without the appraiser's estimate, the performance of the agents can not be measured. There is no way to reward good performance or punish bad performance. The agents are simply collecting their cut of the transaction.