For ID systems, I have yet to find a way to do registration in a decentralized way. Until we get cheap unspoofable genome sequencing devices (which may never be a thing), we will have to trust some authorities.
Once registered, you don't need to trust the Estonian government at all: you get an IC card and a reader (all open source IIRC) and you can autonomously authenticate. If memory serves, you can even authenticate pseudonymously.
Note that you don't have to trust everyone, you have to trust the e-ID registration system as a whole. That is, a single flawed individual won't be enough to corrupt the whole thing.
Which is fine, but than don't talk about cryptocurrencies. These are supposed to be trustless, not trustless-except-we-all-have-to-trust-the-government. Just talk about some new state system that uses some cryptography somewhere.
