Biometric has its own problems. What's a fingerprint but a password you can't change?
Any secret can be stolen, bio or otherwise. The key to robust ongoing identity is not a better shared secret, it's a better way of recovering from theft of shared secrets. One way is to have a big trove of non-secret-but-not-public data, like prevous addresses and employers (which is how the credit bureaus sometimes authenticate people). Who has more such info to draw from than the government? Another is to use shared info that goes stale quickly, e.g. "What magazine did you get in the mail yesterday?" Again, the government, by virtue of being the government, already has candidate info to draw from.
And what if all else fails, if some super-hacker has stolen or has ongoing access to every single piece of digital information that could be used to authenticate you? If you're a startup or a corporation or an open source project, you throw up your hands. If you're the government, you say "Please visit your nearest police department and bring your photo ID and some utility bills."
The more I think about it, the more I'm convinced that this is the only good solution. Like someone else in this thread said, Identity is hard. There's no silver bullet to make it a tractable problem, but you can throw enormous resources at it. And in the government's case, the most costly part (building a brick-and-mortar office in every city, town, village and hamlet in America and staffing it with humans) has already been paid.