My financial advisor claims that his asset allocation has been engineered to provide a higher expected return that compensates for his higher fee. Should I not be willing to pay the higher fee to get the higher return?

While indeed (based on long-term historical data), there are allocations that have a higher expected return than the overall market. Those higher expected returns come at a price of higher risk (in the form of higher volatility or divergence from the returns of the market or both). Aside from diversification, there are no free lunches in investing. The bottom line is that your consent to take on more risk does not justify a higher fee from your advisor.