Ok, so again I ask how this relates to a portable generator. A 32 HP V-twin engine will more than run a whole house generator. Still not a 5 HP lug around generator motor. Yes, if you can advance the timing on the motor, it will run better on 93 octane fuel. Issue is that a small engine doesn't lend its self to having adjustable timing by design. The timing on the motor is retarded on purpose to keep it out of detonation when running poor quality fuel. Manufactures do this to keep from replacing engines run on poor fuel during the warranty period. As far as the specific issue you saw with the heat in the exhaust on your mower, yes. I agree that your changes made were what took the heat out of the exhaust. But it was the timing change that did most of that. If you are seeing the flame in the exhaust, it's obvious that the valve is opening while the fuel is still burning. That results in lost power. And yes, the reason for the timing being late is the ability for the motor to run crap gas. Now, that being said, an engine converts heat energy into mechanical energy. The heat creates expansion of the gasses in the cylinder and THAT is what is converted into rotational power. The reason I say this is simple, if a fuel will make MORE power per gallon in an engine it would be reasonable to think that it burns hotter. You want to bring physics into it, fine. So, dumping 93 octane into a standard UNMODIFIED small engine WILL cause it to run hotter. Especially the exhaust valve. Its creating more heat, and you are dumping that heat across the exhaust valve because the timing issue talked about before. Now, IF you can advance the timing on the motor to light the fuel earlier, then great. That will have a significant effect on the motors efficiency and power output. Problem is that adjusting the timing on a small engine is very difficult, and putting it back is just as hard. So when you are out in the bush, and the only gas pump around says 87 on it, you have to tear your motor all apart to reset the timing. Now, the other side of the argument is this, engine makers realize that there are those folks that will run 93 in their lawn mower. So the exhaust valve on them is made of different steel than the intake valve to deal with the heat of the 93 fuel. Keep in mind that some old engines were just prone to belching fire. I have a 53 gravely that Looks like the burner of a gas stove at night. The fire is that constant and that blue. This is with in just running above idle. It's very old in comparison with a briggs on a current production mower. But it was made in 53 so it's 60 some years old. I doubt that todays Honda engines will be running in 60 years.
You make a thoughtful argument but have your facts wrong. First 93 octane does not burn any hotter nor does it contain more energy (as measured in BTU's per gallon of fuel). Higher octane fuel burns a bit slower and has a higher preignition/detonation threshold. Many tend to think that a gas engine runs from explosions in cylinders but such is not the case. There is a burn when proper fuel is used and the key to peak efficiency and output is developing peak cylinder pressures at optimum rod crank angles for maximum power transfer. When 87 octane is burned in a modern car there are vibration sensors in block tune to frequency of detonation that sense it developing before you even hear it. The computer will regard timing to prevent it but that will also reduce peak pressure and optimum rod to crank angles so less power is transferred. The car owner is happy because car does not knock and burning cheap fuel and oblivious to the fact it is actually costing them more to operate on cheap fuel.
In the case of a air cooled engine, in old days they were flat heads with compression ratios of 6.5 to 1 or so. With the birth of OHV air cooled engines they efficiency was increased not only because of improved volumetric efficiency but reduced heat loss with smaller chamber surface areas. They also raised compression ratios to the range of 8 to 9 to one. This on a warm day the use of 87 octane will result in engine being on verge of detonation under load and there will effect feel of engine. With 89 there is no tendency for this and engine will run smoother. Many do not realize that the true octane requirement of a engine is not a constant as it varies with air temperature and humidity. You want to use minimum octane needed to cover these needs.
On this nonsense about engines running hotter on 93 is pure BS. If engine is close to detonation it will run cooler. A gas engine is a heat engine using energy from expanding gasses which cool as expanded. The closer that peak pressure occurs to just after TDC, the more expansion of gas is converted to HP and greater the efficiency.
In next few years you will see wider use of akinson cycle engine which are more efficient but develops less HP per cubic inch. Its magic is that it uses a very high compression ratio of 13 to one or more but it leaves intake valve on for a bit on compression stroke reducing effective compression and risk of detonation. But, the 13 to one CR provides much greater expansion on mixture after burn capturing more energy and end result is exhaust is much cooler too than a normal gas engine. The Toyota Prius uses this in its engine design and it is one of the reasons for its outstanding economy.
In a nutshell there is a lot that people do not know or take for granite when they use their cars. One reason diesels gained a lot of ground for many years was they had lack emission requirements and had one fuel type to work with. Gas engine design was hampered for years by emissions before technology made it practical and the existence of 70's era 87 octane fuel that it must tolerate. If there was but one fuel, 93 octane, there would be a different generation of engines with better power and efficiency but such is not the case as long as the holy grail of fuels, 87 octane exists. E85 has a octane of over 108 and could use a effective CR of 13 to one and more for more power than possible with 93 and economy approaching that of current gas motors. But once again being able to tolerate 87 octane removes option....