Drew, the ordinary homeowner rotary power mower pretty much "eliminates the flywheel." It's there, but too light to start the mower with nothing on the other end of the crankshaft. It provides the ignition magnets, cooling fan, and no doubt some flywheel effect along with probably some balancing. But it needs the blade to even get running. If you want to run it with say a belt drive and only a pulley, the engine builders sell "heavy flywheel" versions.
Boliy... I was impressed when they came out and early reviews were good. Nearly everybody soon seemed to go sour on them. Think I'd avoid.