It is based on the usual readily available circuits.
In the US, the standard residential receptacle is 15A @ 120V. That's 1800W. Actually, many devices are limited to 1500W due to 80% maximum use for continuous operation. There are larger circuits available, which would work better, but for portable appliances 15A @ 120V is the only thing you can really count on, so that is what the manufacturers make.
In Europe, voltage is roughly double - typically 220V, 230V or 240V, with varying amounts of current available. But with a typical 12A available (often more, but we'll use that as an example), that allows for 2,600W or more (depending on voltage). As a result, instead of making devices to the maximum of the circuit, they can be built to a desirable size based on usage (how much stuff you want to heat up and how fast you want to heat it).
In Japan, the voltage is 100V, even lower in the US. If devices are designed similar to the way they are designed for the US (which is a lot closer than Europe's 220V+), then 1400W or so is typical. The US numbers are actually often based on 125V. 1800W/1.25 = 1440W. There are a bunch of other variables, but that does tend towards a typical value of 1400W.
And yes, "wires heat up" is a key. Larger wires can safely handle more current, but they also cost more. So 15A-ish circuits (13A, 15A, 16A, 20A) are typical all over the place due to wire sizes, so voltage ends up determining the total power.
Since most circuits for small appliances really don't need much power, it doesn't matter much. Except for things designed to generate a lot of heat as their primary function:
- Bathrooms - hair dryers and similar items
- Kitchens - hot plates, toasters, electric grills, microwave ovens
- Space heaters
It is possible in the US to install 240V receptacles for more power, but since the typical house doesn't have any of those in the kitchen, manufacturers don't make them.