There are also alternatives that can be good enough, such as the Swedish BankId system, which is managed by a private company owned by many banks. They provide authentication and a chain of trust for the great majority of the population on about all websites (government, healthcare, banking and other commercial services) and is also used to validate online payments (3D Secure will launch the BankId app).

While it's not without faults (services do not always support alternative authentication which may support foreigners having the right to live in the country), it has been quite reliable for so many years.

So just to say, you can have successful alternatives to a government controlled system as many actors may decide it is quite valuable to develop and maintain such a system and that it aligns with their interest, and then have it become a de-facto standard.