IMO this is another non-sequitor.
Let's say you had a digital ID in the form of a smart card for your SSN with a USB connection that was required to be plugged in when you auth'd to a government website to file your taxes. No new number would be required for a digital ID card in the US. Tax return fraud to get people's refund sent to someone else, though? Probably down! Does everyone have an SSN? Who cares, let's improve things for the vast-majority case where we have an extremely insecure little piece of paper.
That smart card doesn't magically reconcile and rationalize the sprawling hodgepodge of government systems.
Or, let's go the other way: not having a digital ID card does not prevent the government from rationalizing and tying all those systems together.
You might look back to the recent past when the executive branch sending employees to all those disparate agencies to grab that data and make changes to those systems! They didn't need a new digital ID to do that, and they wouldn't need a new digital ID to improve the use of SSN-as-PK-for-cross-system-joins.
Being more rigorous about tracking the existing numbers already assigned to you does not require smarter, cryptographically-sound, identification tokens. And those tokens do not require the government improve their processes for connecting things *after the "give us your SSN for identification" of their various separate web-based services (or the non-government entities that also use those SSNs) that people love to abuse for fraud.
Nor does any of this make it easier or harder for the government to take "absence of evidence of identity or citizenship" as "evidence of absence of identity or citizenship" - if you fit the non-citizen profile, the burden's already on you to prove it, and what makes you so sure that the courts wouldn't happily let this or a future administration expand the boundaries for "we picked you up because we were suspicious, now YOU have to prove who you are if you ever want to get out" regardless of if a digital ID card exists?