I'm not sure of the rationale for not running excessive unloaded speeds or not idling a lot during break-in periods, but I can tell you this...
The oil in the gas mixture provides the only lubrication there is in a two cycle engine. The richer the mixture (air/gas ratio) the more lubrication you have. That's why when you adjust the high speed mix, if you do it 'unloaded' you need to richen it up til the engine starts to "bog" or load up just a bit. As others have pointed out, the oil/gas ration will also determine how much lubrication as well. During break-in this lubrication is very critical as you have a lot of metal wearing away because everything is still very tight. (Which of course, generates a lot of heat - which could be one reason you don't want to race the engine much during this time. That high RPM generates that heat and wear that much faster. The pressures on the rings are much greater at higher RPM. So naturally they push against the cylinder walls harder and there will be more wear. If you want to check a car for engine wear, one of the things you can do is find a good hill and charge up it to see if you can spot the "blue smoke". You don't want to wear out your rings and cylinder prematurely by racing the engine.
In addition at a high RPM you're burning that much more fuel which.. adds more fuel to the fire... (Sorry 🙄 ) which generates more heat, which of course you'd like to avoid.
Idling on the other hand is not so good either. It tends to cause the engine to run "dirty," as in incomplete combustion, which means carbon build-up, which in turn can cause wear from an abrasive substance, and plug fouling, which makes the engine run worse which in turn causes incomplete combustion... and so the cycle continues.
In a 4 cycle engine, the idling, stop start kind of running (especially in colder weather) isn't very good for engines because if the engine doesn't heat up enough, gasoline will condense on the cylinder walls washing away the lubricant. Since in a two cycle the gasoline carries the lubricant, I'm not sure what effect this would have...
So if you don't have instructions for the break in period, see if you can get some.
I'm actually a little surprised it took that long for you to get the thing running though. One of the things a Mac chainsaw tech told me once was that if you saw a lot of broken starters it meant that the engine was hard to start... So don't be surprised if those blisters turn into a starter rope or spring...