It's not the same issue. The vast majority of kitchens in the US have 20 amp circuits (so 2,400 watts peak, 1,920 watts continuous) exclusively. It's a bog standard receptacle (NEMA 5-20R instead of 5-15R) that's backwards compatible with 15 amp plugs. In fact these days most 5-15R receptacles have identical guts to their 20 amp counterparts save for the additional provision for a horizontal blade.

The electrical code (NEC) has started moving towards requiring 20 amp circuits in other rooms and more 20 amp circuits in kitchens.

But they're staying shy of the amp limit on purpose. So designing for 20 amps would be somewhat of a boost but not enough. While doubling voltage would actually fix the problem.

You're going to stay below the circuit breaker rating no matter the voltage. Nobody's going to put a 2,400 watt heater in a dishwasher designed to be used on a circuit that tops out at 2,400 watts because:

a.) I'm going to go out on a limb and suggest that most countries will place limits similar to the NEC's 80% rule.

b.) There are other high current draw devices in a dishwasher that will have to run concurrently like the water pumps.

Same with things like electric kettles. You're not going to find 1,800 watt kettles in the US even though they're designed for circuits rated at that. A quick peek at the kettles available in Australia show that most top out at 2,200 watts for the same reasons.

In the context of a dishwasher 240V would only get you more powerful heaters than you could run in the US if the circuits were rated at more than 10 amps. Voltage isn't the issue.

You know what, I didn't read the middle comment in this thread closely enough before my first reply. You're right that an Australian circuit doesn't help much, and the voltage on such a circuit is useless.

A UK circuit on the other hand would fix everything. It has the same number of amps (or maybe more), but double the voltage.

The problem isn't purely amps or volts, but in general home circuits tend to have a similar number of amps, and higher power usually goes hand in hand with higher voltage. That's the sense in which voltage fixes the problem. A US appliance staying well within amp limits has a lot less power than a UK appliance staying well within amp limits.

Meanwhile, here in Germany, we have 230V, but every standard wall outlet is rated for 16A continuous load over 1 hour so you can get 3.6 kW on each circuit.

Your standard home has a supply of 3 phase power @ 35A (southern Germany) or 63A (northern and western Germany), I think only the former GDR is at standard 3x25A, because like in many former Communist countries they had to save on expensive copper and aluminium, and since a lot of the GDR was heated by steam-based central district heating systems, you didn't need that much power anyway.

Lot's old homes and flats here limited to 5A or 3A 220v. If you don't use electric heating your power demands go down substantially, though 3A is a bit small these days.