It's possible these is carbon build up and the engine requires a higher octane to prevent preignition (caused by hot spots in the carbon build up), in which case the higher octane is a band-aid for the build up.
About the mpg improvement , especially across that variety of different vehicle/engine types, I've been around cars the better part of 3 decades, a mechanic most if it and restore or assist in restorations of classics, never actually seen that (mpg gains due to higher then required octane) happen before. I have seen people swear by many different things that actually do not nor can not occur, some of that due to some of that from wives tails, some from old techniques that USED to applicable (mothballs in the gas tank is one ofthe biggies, more later), some due to the fact that some product or service cost big bucks so it 'just has to be better'.
Also, in areas that have this reformulated gas can use "UP TO" 10% ethanol. Ethanol contains less BTUs per volume then straight gasoline. In some places even from the same companies, the amounts of ethanol between grades can very. MPG can easily, easily drop 3-5% with a 10% ethanol mix from the same octane rated fuels. About 20-25 miles from me the stations do not have to carry the ethanol mix. When my travels take me that way I try and make it there with almost no fuel and fill up there. Combined driving my GTP (supercharged Buick V6, mildly modified) gets 24+, highway steady 70 it gets 28.x. With straight gas combined goes up 2mpg, highway it goes up 4-5 to 32-33+ mpg. My Caprice (modified LT1) goes up from 21 combined to 24 and 26 to 28+ highway. Same exact octane, even the same brand, difference is just the 10% ethanol mix to straight gas.
Flawed testing is another thing that skews results. Your chain saw example is a perfect one.
You say the new gas is bad for 2 strokes because in ONE SINGLE instance you had a problem. Did you try that exact same batch of premix in several other 2 strokes? Did you try another brand of 'new' gas with the same oil? With different oil? The gas can could have been contaminated, the chainsaws tank could have been contaminated, something in the carb or ignition could have been stuck, jarred loose when you dumped what you perceived to be bad fuel. Dozens of variables that were over looked by simply dumping one tank of gas. Thus you can not come to the conclusion the new gas is not good for 2 stokes.
A major point your also overlooking, the millions of people that do not have any problems with new gas in their 2 strokes. I some areas that the ONLY type of gas we have. Myself, neighbors and friends with everything from cheap off brand to top end 2stroke, lawn mowers, chainsaws, string trimmers, leaf blowers, hedge trimmers, etc etc, have nary a problem due to the new gasoline.