The Caterpillar link I provide above does describe problems with gas engines.
But we know car engines are designed to idle in traffic, and to operate around 10 to 20 HP while having peak 100 to 300 HP.
Is this with or without battery & inverter?
If an inverter can start the A/C, then generator only needs to supply running power, not starting.
Could a generator be rigged up with a very heavy rotating mass, to provide surge?
My HF chipper has a large, heavy steel disc. Very different feel when rope starting vs. most power tools.
When chipping 2" branches, that flywheel is what does it. If allowed to suck in the branch it does so too fast and slows to a stop after a number of turns.