Having an ID card makes life so much easier on so many levels. For example, I have my Polish ID card on my phone, and I can do almost everything with it with the exception of crossing national borders. It's not obligatory to carry ID on a daily basis, but citizens even have the ability to verify someone else's identity using our mObywatel app. I bumped into some poor bloke a couple of years ago, and with mObywatel, I could show him everything - my identity, my driving licence, my car insurance.
What's useful and handy is that these things are also available to the police. If you're stopped for speeding, we have no such thing as a "producer", you just give your personal number (like an NHS number) and the police can pull up everything - your photo, name, address, everything.
Likewise, if I want to open a bank account, deal with some company administration stuff or even just pick up a letter, the ID card (or mobile ID) is more than sufficient. Things like utility bills are unheard of here, and both my British and Polish passports stay firmly locked in a drawer at home because they're simply not needed.
Even when I went to apply for my Polish passport, all I had to do was show my physical ID card and give them one photo. The rest was all done electronically, no need for paper forms, and I had to sign my name on a tablet after confirming the data they held on me. I actually saw a mock-up of the passport information page, so I could verify that my name was correct and so on. Compare this to the nonsense of sending birth certificates and so on!
The critical thing is that it's not mandatory to *carry* the ID.
And if those, presumably Andorra has pretty universal ID coverage de facto if not de jure since you’d need something to be able to leave the Principality (although the chances of actually requiring it on a short hop over to France or Spain are of course pretty minimal).
On the contrary! Andorra isn't part of Schengen, and there are full border controls between Andorra and the neighbouring countries. In practice, France focuses more on identity controls while Spain focuses more on customs controls, but it's not abnormal for both countries to ask for ID there. It's actually quite a problematic situation, because anyone visiting Andorra with a Schengen visa needs a double or multiple-entry Schengen visa. There's also a problem at the moment caused by the fact that Andorran residence permits are not valid for entry into Schengen, so someone in Andorra who isn't legally able to travel to Schengen countries is effectively stuck there. In practice, what happens is that if you need a visa for Schengen, then you have to get a long term visa for Spain/France and then get new ones on the basis of requiring it to leave Andorra.
Andorra generally only does random identity checks in comparison, and they don't require visas from anyone. This situation has caught out quite a few people, as for instance, Brits need to get stamped out of Spain/France and then stamped back in if they visit Andorra.
But going back to the ID issue: so many things in the UK are needlessly complicated because of the lack of ID cards. Things like renting a flat: here, again, it's standard to just show your ID card. No need for anything else, the ID card (and the ID card number) is more than enough to verify everything about you. Things like providing utility bills are just absolutely unheard of, you just need to know how the ID looks and it's more than enough.