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.
Except technology makes it possible to constantly send get requests to everyone not carrying it. The limiting factor here was how much time police was willing to waste.
Slippery slopes work exactly because people are incapable to predict the long term consequences for eroding safety standards and are at the same time arrogant enough to believe to be very much capable. Its cognitive biases at work in selecting some of the most reckless approaches for dangerous situations.
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.