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Do they? The IKEA ones are rated for 3680W, which is plenty even for an appliance on a dedicated 220V 16A circuit.

My understanding, and I would love for someone to explain why, is that they measure current with a shunt resistor which is fine for inductive loads like a water heater, but not fine for a big motor for example.

IKEA's smart plugs are all rated to carry the full wattage allowed by their plug types for resistive loads (though only 300W for motor loads)

You could use the smartplug with a relay to a higher capacity non smartplug.