ID card is mandatory by law, but there aren't sanctions (in my knowledge). You need some kind document though, in US that is usually drivers license. I don't see big difference here.
In the US you are required to have your drivers license while driving, but I do not believe there are any blanket requirements (since it would vary from state to state) that you must be able to furnish identifying documents at all times.
Documents are two way streets. You need them to prove your rights. You need document to prove your identity to bank or notary. If you are younger side, document helps validate your age in liquor store.
I trying use "american" examples here, but other countries can have other regulations or customs. Document, especially digital one, is very useful.
For example, I like do encrypt with id card, when sharing materials over untrusty medium. You don't need worry about key exchange, you don't need to teach or install software to other party devices: they already have knowledge, how it works.
It's also very comfy that I can send digitally signed documents and that isn't fringe thing, there is knowledge and bureaucratic processes, how to handle it.
I take the view that rights are inalienable, I don't have a problem with documents but with Id cards.
Given the structural deficiencies of the US police (And other police forces) giving them an excuse to stop people is to be avoided unless strictly required.