By the same token running grossly too high of octane for an application will result in reduced performance as well.
If an engine is designed for 87 octane and you use av gas (100LL) you're leaving unburnt fuel as the engines compression ratio and valve timing don't allow enough time to fully burn the slow burning higher octane resulting in less power.
Will you notice a tank of premium in a 87 car? Not likely but you're loosing power the other way compared to low octane.
Again none of these are absolutes, rather generalizations as AFR, ign timing, cam height and duration, piston design, compression ratio, temperature all play some roll.