I don't think reducing the conversation to a binary state really furthers the conversation in a productive way.

The government already does deploy tech services with varying levels of cooperation with the private sector. "MyCRA" login is a prime example: you don't NEED to login with credentials governed by the CRA, you can optionally authenticate with your bank which may be easier.

If they ONLY relied on banking authentication, that creates an obvious surrender of a critical piece of the service infrastructure.

"Nationalizing" services in part or entirely is a discussion that can be had without reducing it to "but Intel makes the CPUs and they have private sector interests so unless the government makes chips then it's a doomed endeavour"