This is a simplification of the problem. The issue with CPC bidding is that you're in a dynamic marketplace with competitors entering into it everyday. Maximizing profit is rarely what you want to do. Sometimes you want to bid before the maxima (to avoid encouraging competitors to bid it up), sometimes you want to bid after the maxima (to acquire customers before your competitors do).

It also assumes there is only one smooth curve that goes up to a maxima and then down again. In reality, there are local maximas that are worth considering.