Here's the waveform from an open frame Genset
And here is what your appliances and electronics really want.....
The difference is THD and surging.
To the best of my knowledge......
The biggest problem with non inverter generators is power surges. Those can zap electonics. A lot of electronic components have specific voltage tolerance ranges.
Non inverter generators must run at a specific RPM to create the Hertz needed. In the US that is 60Hz...and that speed is exactly 3600rpm.
Because motors on generators are often not precisely governed, but instead use springs or simple governing methods, electrical spikes occur when the motor stumbles for example then surges to recover..
So a non inverter generator with a sophisticated speed control system would work better, but still not as good as an inverter generator.
I would venture a guess that your Generac non inverter generator has a better speed control system than my Coleman Powermate circa 2004.
The other problem is Harmonic Distortion, which causes an increase in Current, thereby creating heat. Heat is the enemy of sensitive electronics.
Electronics were designed to operate on Sinusoidal current. The further from that, the greater the THD. I don't have samples of power quality in various countries but
it is likely that most developed nations have the capability to generate AC power with THD of 6% or less, the generally accepted threshold of clean vs "dirty" power.
Again, not all generators are created equal. If you buy a high end NON Inverter generator with precision electronics and a high quality alternator, your power is probably less "Dirty"
that less expensive non inverter generators. 10-15% THD (or more) is common in non inverter generators.
So it's probably not completely accurate to say "appliances will be damaged" by non inverter generators, but maybe it is more accurate to say it is less likely that appliances will be damaged by non inverter generators. Or that Inverter generators are more likely to provide AC that is within the specifications required by appliances.
No doubt, to some degree, most quality appliances have some built in filter circuitry to help suppress some of that. However, above 6% even the filtering circuitry will suffer from additional heat.
YMMV (And an EE can certainly correct me as needed)
Harmonic distortion can have detrimental effects on electrical equipment. Unwanted distortion can increase the current in power systems which results in higher temperatures in neutral conductors and distribution transformers. Higher frequency harmonics cause additional core loss in motors which results in excessive heating of the motor core. These higher order harmonics can also interfere with communication transmission lines since they oscillate at the same frequencies as the transmit frequency.3 If left unchecked, increased temperatures and interference can greatly shorten the life of electronic equipment and cause damage to power systems