A couple of minutes running like this with an air cooled single is plenty of time. I then let it cool completely and perform a compression test so I can use the information as a benchmark to compare against some time later. A static compression test is kind of like checking the blood pressure of the engine - it checks its current state. In either case, even if the compression is fine and the hours have stacked up - change the piston and associated parts out at a specific interval. For this engine I feel safe with 45 hours.
Metals are elastic materials that can only withstand a certain number of stress cycles.
Going beyond that number is not wise. Some oil injected engines require a small boost of oil - by adding it to the raw gas. I have seen the additional oil requirement on a few engines - the Suzuki LT80 comes to mind as well as the Yamaha GP760. As it is right now the interior of the engine was assembled using a very light coat of two-stroke oil on its piston and associated parts, B.E. and main bearings and cylinder wall. There's more than enough oil available for start up during the kick starting procedure.