If they come in too low on the purchase price, then it kills the deal, and everyone is unhappy. The seller didn't get their money. The buyer didn't get their home (though in many instances they shouldn't be unhappy about making a poor investment). The lender and agents are unhappy that the deal isn't closing.

If they come in too high, then they could be potentially held liable for that surplus amount. Any party to the transaction could go after them in court if/when the market changes, and the lender is raising lots of questions about the report.

If you are a person buying or selling a home, and the appraiser comes in right at the purchase price, what difference is it to you? The deal closes, and you are happy.

Every once in a while I see someone on this board vent their anger/frustrations about an appraiser who ruined everything because they didn't come in at a value that was high enough, but if they were appealing their property taxes, they would be more than happy to use that appraisal.