A typical German water heater, e.g. from stiebel eltron, will be between 15kW and 22kW at three phase 400V, which is obviously too much for a regular outlet. Which is why it's usually wired directly, the same as stoves/ovens tend to be.
https://en.wikipedia.org/wiki/Split-phase_electric_power
Three phase circuits are 120 degrees out of phase.
But completely agreed that three phase 400V seems crazy!
Ok, help from our new common friend:
Yes, your statement is essentially correct. In the United States, residential electrical supply is typically a single-phase, 240-volt system that is "split" into two 120-volt legs. Each of these legs are 180 degrees out of phase with each other, which allows for both 120-volt and 240-volt circuits within the home. This arrangement is often referred to as "split-phase" electricity. It's not technically two-phase because a true two-phase system would have two waves offset by 90 degrees, not 180.
In the US houses get 1 of the 3 phases. That phase is split in half, and so each phase is 180 degrees. This is different from 3 phase power where each phase is 120 degrees. 3 phase is good for a few things, but for a water heater it doesn't matter, and most of the things 3 phase is good for you today will run off of an inverter for speed control which in turn can run off of single phase (3 phase is still better but only because you can use smaller capacitors)
Tankless water heaters are much more common in rental apartments, and Germany has one of the highest quote of people living in rented apartments. And if space is at a premium, of course tankless heaters are preferable. Apartments are also the reason why electric stoves (again, using 400V tri-phase) are so popular in Germany.