Amperage determines how much current something gets.

Voltage times amperage determines the power something draws.

More current needs thicker wires, while higher voltage does not.

Power is what matters, and power (in watts) = current (in amps) times voltage (in volts). US residential power outlets are 110V and typically cap at 15A, for a power output max of 1650W. But it's also pretty common to have 20A outlets in kitchens, which would max out at 2200W. Still, there aren't a lot of 2000W kettles in the US, and it's pretty standard for the ones you'd buy in a store to only draw about 1500W.

Meanwhile, in the UK, the standard outlet is 230V, rated for up to 13A, for about 3000W. And culturally, in terms of consumer expectations in the UK, the kettles are generally designed to max that out to use the full capacity of that outlet.

So on average, the typical US kettle is only about half as powerful as the typical UK kettle. It's a combination of the US electrical norms and the cultural/consumer expectations, because it is entirely possible to have a 2200W kettle on a pretty standard kitchen circuit in the US.

Find an electric kettle in the US that works as well as one in the UK? They don’t exist here.

Yes they do.