A nonprofit business could do this if backed by all existing dotcom and bitcoin billionaires. But they’d all want to profit from it, so either non-profit (NGO) or governmental it is.
Fun fact: this is already a core function of USPS. They serve as an identity verification hub for both US passports and their informed delivery and PO box services. They just have a human-dependent process rather than an identity-generator booth. So they’d be perfectly positioned to take your ID, hand you an attestation request QR code, and get your identity-signatures on it — without being able to reverse-engineer your biometrics from those signatures, but still being able to detect gross variances when someone else tries to lie about being you in a future verification.
Anyways, none of this will likely ever happen, but the rich tech folks could make it happen at any time if they cared to. Instead we get THE ORB which is doing retinas as a for-profit without auditable artifacts or hardware. Sigh.