And a puny domestic inverter will die horribly if it stays on too long.
The semiconductor electronics are certainly capable of that but the transformer will saturate and then get hot ultimately catching fire if the frequency drops too low. Some US kit built for 60Hz only would get awfully hot on UK 50Hz mains. A cheap and nasty US brand of shavers sold mostly at Xmas relied on a 60Hz mechanical resonance for good measure.
Japanese kit can pretty much always be relied upon to work on either 50 or 60Hz since roughly half of their country is on each frequency.