It is not always true that the price a buyer is willing to pay, i.e., market value, is going to be higher than an appraisal nor is it always true that an asking price is going to be higher than an appraisal. An appraisal is not normally requested or performed until after a contract is signed and a mortgage is requested. They are customarily requested by the lender. Thus a selling price is normally set prior to an appraisal.
An appraisal is an "educated and technical" price evaluation by a trained and licensed appraiser, whereas, most selling prices are determined by a CMA (comparative market analysis) performed by a Realtor and a meeting of the minds between that Realtor and the seller. So, even though the processes are similar, the "appraisial" is considered by lenders to be more accurate, thorough, and a better representation of the true value of a property. It will govern the lending amount.
I am an Accredited Buyer's Representative and do not write contracts without an appraisal contingency. It is for your protection because if that contingency is not present and the home you are purchasing is appraised at less than the agreed price (and you are past your due diligence period), you will be required the provide the difference out of your funds. If you did not have the additional funds and voided the contract at a minimum you would lose your earnest money and if the seller chose they could sue for performance.
Bottom line - never assume the asking price will be the same as the appraised price and always include an apprasial contingency in your contracts.