I've never had one that wasn't connected to the hot water line.

If you've got both available, I can't see any reason why you'd choose to hook it up to cold. That just means it takes longer for your dishwasher to heat up.

Well both are not always available. In many countries, there is no hot water tank/line. There are only inline heaters or very small tanks locally where needed (each bathroom and kitchen sink). Then, you buy appliances such as dishwashers and clothes washers that also have inline heaters built-in (and you don't need to think about this, in such a region, this is the default thing that is sold).

It doesn't necessarily take longer to heat up, they are pretty much instant since they are designed to heat as needed locally as needed (don't need to heat a large volume of water) and they are at least as fast to provide hot water as a central hot water tank. They can be gas or electric powered depending on what is available/cheaper in the region and you never run out of hot water with an inline heater.

Even if you do have a central hot water tank, it's possible that heating water locally at the dishwasher is faster depending on distance to the tank. Anecdotally, I used to wait for hot water in the kitchen when I lived in Canada and I no longer do in Europe where I have no central hot water tank. In North America, recent high end home kitchens feature a local inline heater for hot water at the kitchen sink even though a central hot water tank exists.

If it takes x gallons for your hot water to run through, and your dishwasher only consumes <x gallons before stopping long enough for your hot water line to cool again, then connecting your dishwasher to your hot water line would both waste hot water and never get any.

Our dishwashers in Europe must be connected to cold water (I just checked a manual)