I posted the question of what bad things happen when you start and stop under load over here:
https://www.smokstak.com/forum/showthread.php?t=186387
These guys are experts on Onan generators.
Basically, it's bad to start and stop under load for two general reasons:
First, you can get erratic power generation on startup and shutdown that can cause issues for electrical devices being powered.
Secondly, you can stress generator components as they try to compensate for the changes in power output that happen during startup and shutdown.
This doesn't apply to all power generation systems; Some have safeguards in place to protect against these conditions. But, unless you know for sure that yours does, it's probably a good idea to start up with minimal or no load, and shut down with minimal or no load. Personally, I don't go so far as to open and close the breaker - I just make sure that neither the AC or the microwave is running. And I let the generator warm up for a minute before I turn the AC or microwave on.