Comment by lxgr
But GP raise a valid point: If IDs are ubiquitous and commonly used for non-government business, the government does implicitly gain substantial "veto power" over non-government transactions (by revoking existing credentials or not issuing new ones).
Availability has to be ensured just as much as security and privacy in such a scenario, and that's not trivial. (I still personally think it's worth trying.)
In those places where a system like Sweden's has been implemented, the usage is constricted to certain areas. And in the case where it's used elsewhere, that's an option that is not mandatory (and in any case far and few between). A way to identify an individual is typically related to financial or contractual issues. So far, at least. Looking at you, the UK