"Higher octane" only means more knock-resistant. It does not mean "harder-to-ignite" or "hotter burning."
A gasoline engine will not perform worse in any way on higher-octane gasoline. The higher-octane outputs of a gasoline refinery have only been reformed to be more knock-resistant. They still have to meet the same volatility, detergent, oxygenate, and other parameters as do "regular" gasoline grades for the same market. (And if you want to learn about all of the characteristics that are optimized and regulated, this technical review is fantastic.) In fact, you're likely to get a tiny (less than 1%) boost in mileage because the higher-octane C4-C12 isomers tend to be denser, so the higher-octane gasoline contains more energy per unit volume.
In theory it is possible for higher octane fuel to be less desirable: Ethanol is an octane booster and oxygenate that is significantly less dense than hydrocarbons. (Ethanol is also hygroscopic and can be corrosive to fuel system components not designed for it.) Given a choice between a fuel of adequate octane for one's engine, or the same fuel with its octane raised by blending with ethanol, one would be wise to buy the lower-ethanol blend. However I am not aware of any markets where premium gasoline contains higher blends of ethanol than the adjacent pump grades.