The main issue with what you're talking about is that from a mathematical perspective, 'average' already has a strict meaning, and in this context nearly always means 'arithmetic mean'.
If you want to talk about another measure of speed, you have to drop the term 'average speed' at the very least. What your method seems to be referring to would be something like the average of multiple constant interval average speeds, and as such two people both reporting their AoMCIAS could vary wildly, even if they traveled side-by-side.
For example, why pick tenths of a mile? There are infinite variants of division lengths unit choices such that two AoMCIAS numbers can't even be related (unless the distance has been mutually agreed upon before measurement collection). Good luck getting the U.S. to adopt the metric system or the rest of the world to adopt Imperial units, so at minimum you'd have U.S. bicyclists reporting it over 0.1 mile intervals and everyone else at, perhaps, 0.2 km intervals.
For that matter, why use length as the interval control? If you use a GPS, it's storing the data in semi-regular interval time units (depending on the unit and resolution setting), perhaps someone else tries to unify the U.S. with the rest of the world and proposes 10 second intervals as the new standard.
The result is that AoMCIAS speed numbers would not convey enough information in and of their own value, like averages do. You'd have to report them as "24.56 miles/hour AoMCIAS over 0.1 mile intervals", and that value would vary so wildly by interval choice that it could ONLY be compared to other AoMCIAS speeds with the exact same interval. There wouldn't be a static conversion that could be done, either, you would need to completely resample the intervals from raw data, if it was even available.
All of this is completely independent of it's relevance as a speed measure for bicycling (I have a mathematics degree, and don't time any of my bicycle rides). What I mean by this is: it's possible that you could devise a creative method such as AoMCIAS with an ideal interval distance or time such that the number reflects something more accurate about bicycling performance, and it may even be useful inside of the bicycling context (and likely ONLY the bicycling context). However, it will be of little to no value to anyone else, mathematically or even quick comparison-wise in colloquial speech. Two numbers could only really compared with equivalent intervals, and any ability to do neat things quickly in your head with such values would be relegated to special calculators, computer programs, and perhaps some genius savants.