This is incorrect. In any mode, they are capable of their full rated wattage. At maximum output, the engine is turning the same RPMs regardless of eco mode or not (it's actually 5000RPM or so for almost all of these smaller units at maximum load). The only difference is that it lowers the engine speed under no/low load, the inverter itself does not have its output limited. The inverter is always "working". There is no time when these function like a standard brushed or brushless generator with the output connected directly to the windings on the generator head.You should look at the manual before buying an inverter for the max draw under “eco” mode, which is when the inverter is actually working. When you exceed that they revert to a standard generator running at 3000rpm negating any fuel savings. My cheap WEN is at 60% of its 3500W constant rating.
I measured all the max surge on things I would run with a decent clamp meter and a cord with individual conductors. I was actually surprised by the surge on some things. I have a 6500BTU A/C that surged to almost 18A one time. I guess it’s for a very short time because it doesn’t flip the breaker.
You are correct however in that the surge under startup of a large motor could put some stress on it as unlike a regular generator you can't rely on the rotational momentum of the rotor to overcome startup surges, but the inverters contain a capacitor that can help bridge the slight gap to the engine speed increasing.