I used to race karts for years, 100cc and 135cc air cooled, and 80cc and 125cc water cooled dirt bike motors. One of the best ways for a two stroke nut to get their fill of the smell of castor oil.
Anyhow, as to the ways and whys of making power in a two stroke, or not, here is what I've learned and seen over the years.
The pinnacle in single cylinder gasoline burning two strokes can be argued between the camps whether it was the Intercontinental A class racing kart engine, a class that was sadly discontinued. The engines were 100cc, and the final derivation was liquid cooled pumping out 30+hp with a peak rpm of 20,000. The air cooled engines weren't far behind, but there is plenty of cooling on a kart that is running 50mph. The pinnacle in gearbox is either the GP bike or the International C kart, liquid cooled 125's that are putting out about 45 hp and revving to ~14,000 rpm. MX 125's can be tuned to put out 40hp by bumping the compression ratio and playing with the porting, and typically the power valves are plugged. Power valves aid low to mid range power, they do nothing for peak power. Also all these race engines run 110 octane fuel.
The keys to making power are the ability to flow the air/fuel charge into the engine, the ability to flow the exhaust out, the compressio ratio, and the ability to deal with the heat of combustion.
In simple terms, saw engines are designed to maximize power to weight ratio, kart and bike engines are designed for max power. An air cooled 100c kart engine weighs 30#'s, and that is just the bare engine, no fuel tank, no oil tank, no bar, chain, clutch or exhaust.
In the desire to get max hp per pound, saw designers use what can be termed a very over bore engine, i.e. short stroke and large bore. This reduces the length and hence weight of the con rod, and also reduces the dia and hence weight of the crank. Whereas with a kart or bike engine, they run pretty close to a square engine i.e. equal length bore and stroke. The short stroke large bore saw engine does not flow as well as a square bore, and the larger dia piston can't take the same amount of heat nor the same piston speeds.
And finally the tuned pipe. Tuned pipes make a tremendous amount of power, nearly doubling the power of a muffled engine. But it comes back to packaging. Pipes are large and heavy and simply aren't an option on a working saw. It's easier and lighter to gain power on a saw by adding cc's vs. adding a pipe.
It would be interesting to see if an engine was designed using a square bore/stroke and tuned pipe what cc you could drop it to and get 8hp on pump gas. Then compare the weight and size to a saw engine, my guess is the saw engine would be lighter, and definitely less expensive. Speaking of which, when I got out of kart racing in the early 90’s, a new 100cc air cooled engine was running ~$1200, and that was w/o the tuned pipe or header which added another $200. So I’m having a hard time seeing a saw for under $2000 using a kart/bike type engine, not to mention it being double the weight. I doubt there would be many takers for a 40+# saw, even if it put out 20-30hp
