Both 2 & 4 storke gennies (especially at the lower power end - up to about 800 watt) are sold here in Aus - 240V 50 cps is normal mains. Larger ratings seem to be mainly 4 stroke - the small ones have only recently become popular and cheap - Chinese of course...

I vaguely seem to remember that 2 stroke engines do not like running at idle or below a certain percentage of max load for any extended length of time - something to do with damaging the bearings or rings...

Most small motor motor-mowers are designed to 'run at full (manual) throttle setting' when mowing - they have a sorta feed back throttle arrangement.