As well as the Estonia eID system works (aside from that time it got hacked[0] and that other time they leaked all the photos[1]) and how well a digital (non-government) system works in Scandinavia… I have to say… As a Dual British/Swedish Citizen, I really do not trust the UK government. They have proven over and over and over, that at every opportunity presented they will increase their own authority. I don’t belie…
Having a vulnerability is very different to getting hacked though. To date, there hasn't been a single breach of Estonia's ID system itself as far as I know, correct me if I'm wrong? And that's saying something given the adversary is Russia. Reading through your link, the leaked pictures incident was a separate external service that's not tied to the ID system itself.
Most human-related problems around bootstrapping one's identity still remain the same and have to be solved. Electronic identity or not. (Also see the XKCD about the "wrench attack")
But a proper ID system gives a nation the opportunity to rely on elliptic curve cryptography and an EAL4+ SmartCard or SIM. Not on a pinky promise about identity based on knowing some number, some face pics or having a gas bill.
Verizon could still leak your hypothetical future e-SSN. But then it wouldn't be sufficient for identity theft or impersonating you in some places. That's not what would be an "identity" any more.