Sure, also because you're going to pay taxes into that ku (city), and they deal with pension and health insurance, even if you're not a foreigner you're going to have to register.

Your residence card gets updated every time you change your address and you do have to go to the ward office for them to update it, but that's hardly "register at the police station".

Edit:

Most if not all the things we have to do, as foreigners, Japanese also have to do it.

The big difference is we're required to have an updated/valid residence card (ID), while Japanese don't need to carry ID.

I'm from Europe, and in my country everyone has an ID and is "required" to have it so I don't actually see the big deal, maybe I'm just uninformed.