That's OK, that's your choice. I believe most dishwashers will work with either.

My dishwasher is connected to a hot water tap and also heats its own water to exactly the correct temperature... it just doesn't need to heat it as much because it's connected to a hot water line.

Here's the install guide of a random dishwasher selling in Germany right now: https://media3.bosch-home.com/Documents/9000521334_L.pdf

It says to connect to a water source with these characteristics:

* Pressure: 0,05 - 1 MPa (0,5 - 10 bar) * Temperature: max 60°C

It doesn't specify a minimum temperature although I assume it'd have to be >=1°C. But it is clear you can connect to either a hot or a cold water line.

Sure, it optionally supports it, but that's an extra water line that'd need to be run.

And what for? Whether the instant water heater or the dishwasher heats the water, it's still going to be the same amount of electricity, the same cost.

Have a look at the overview on Geizhals.de - Almost all current models have optional hot water intake nowadays (like 95%+ of the models from AEG/Bosch/Siemens/Neff/Bauknecht/Miele). This is to further advance the energy-rating. Doesnt apply to the cheaper manufacturers though.

981 of 1027 models from a number of well-known brands have an optional hot water intake: https://geizhals.de/?cat=hgeschirr60&xf=1069_AEG+Electrolux%...

Whether you heat the water in the dishwasher or in an instant water heater, it's still going to be the same amount of electricity for the same cost.

I think in the US people might heat water with natural gas, which is cheaper, but that's not really the case in most rental apartments in Germany.