I don’t think that it is technically impossible and I don’t think that’s what most people have a problem with. It might be possible, just very high effort, for in most cases (e.g. Wikipedia) very little gain.

I think the problem is exactly that one possible solution is a third party that everyone has to trust with their personal data.

The way thinks work in this country that might mean that a friend of an influential MP sets up a new company as we speak that then will be chosen as the one and only service provider for this verification. For a considerable fee of course. This friend will then find an acquaintance who has worked for a consultancy at some point who will then hire a (maybe British) company to implement the service, they will outsource it to a much cheaper (probably not British) company to implement it. Provided that no one except for the outsourcing company has any idea what they are doing and the money is siphoned off to the Virgin Islands already it might take a while to get the service started and then it does not work.

At this time the government will notice that not only their money is gone, they have to pay more to even get it started and from then on the long chain of contractors need a lot of money on a yearly basis to keep it running.

This is the moment where they turn and explain to the public that from now on they have to pay to use the internet.

Remind you this is a country that only since one year requires identification to vote in elections. But everyone is now supposed to register with a third party probably non government institution to access the internet. ¯\_(ツ)_/¯

They only consolation is that they probably won’t get it off the ground in the foreseeable future.