That's an American thing. Not world-wide. As others have said, outside America the common way is to connect to cold water and use internal heating only.

I wonder if it's because of the inability to draw significant power from an average American power outlet. See also the lack of kettles.

You can install a 240v outlet. Many people have them for certain appliances. but you wouldn't need that to heat water, silly.

European dishwashers have to use cold water because of the way they dry the dishes. In America hot air is used to dry the dishes so we can hook up to hot water. In Europe you can't do that because of the Kyoto agreement. So you use condensation to dry your dishes by piping in cold water.

There's not really much difference between them today. Because Europeans have very small homes by American standards (especially British people that live in sad, tiny, little things) the need for quiet dishwashers was also needed which means lower power. Also power costs more in Europe so more energy efficient appliances were needed so you didn't have food grinders, etc.

But today it's almost all the same. But the Kyoto agreement forces Europeans to hook up to cold water and heat internally and not use a fan to dry but rather cold water.