In Germany we have ID-cards. We are in theory required to have either the ID card or a passport with us t all times - but no policeman has ever stopped me and asked for it. I only needed it within Germany for some paperwork (e.g. applying for passport and driver license).Also it is necessary if I want to get mail which could not delivered to my home from the post office - so nobody but me can get at my mail.
I mostly use the ID card for travelling abroad as most European countries (at least all the European Union as well as Poland, Czechia, Hungary) accept it instead of a passport.
I think a driver's licence does not meet the requirements for a proof of identity as not everyone gets one (e.g. blind people).