Is it not the exception rather than the rule for a country NOT to have the requirement to carry ID?
Many countries accept photocopies of passports so that you can leave the original safely locked up.
Certainly in Hong Kong I have been asked for ID on a couple of occasions when I was a witness to traffic accidents. When I first came here (from the UK - one of the places which doesn't even have an ID system (yet), let alone the requirement to carry it) I was a little uncomfortable about carrying ID, but after 6 years I haven't been ID'd randomly and having it makes a lot of little things much easier (and transactions more secure) than they would be in the UK, so I've sort of come round to the idea.