Except that an engine is going to run the compression stroke it is designed for. Adding a high octane fuel doesn't magically change the compression ratio of the engine. And, more octane only means it is more resistant to pre-detonation under compression - it doesn't mean there is any more or less energy available in the fuel, it just prevents high compression engines from "pinging". The one exception is if the engine is so old and filled with carbon deposits that it is over-compressing and pinging, in which case the octane boost will prevent the pre-detonation from being over-compressed.
This is why turbo and supercharged engines need to run premium - they are designed to use higher compression. People putting premium in naturally aspirated engines that don't require it just don't like money, or have been completely misled by marketing that tries to equate octane to "running cleaner".