In the text says it clearly: you must have an ID, and you have to present it if requested. That does not means, you have to have it with you at all times.

Exactly this is the kind of fine details that a lawyer distinguishes in the law.

So no. Absolutely no. You do not have to carry it with you. If it comes to the need, then maybe the police have to scort you to your home and you have to show the ID. But you are not requested to have it with you at all times.