Or you could use Canada as a pattern, and cut hospital admin overhead to half what it is in the US. That is only hospitals. Add in the overhead from every other vector of health care. Then add in the administrative costs of the insurance companies that the provider's overhead sends the paperwork to, when they are done shuffling it.

We need to start somewhere. We may as well start with the functions that contribute nothing to patient care.

This isn't about "starting somewhere" - it's about there not being anywhere near enough cost savings from reducing administrative load to materially pay for these systems. The way you reduce administrative costs is the simplicity of only having one provider. It's just not big enough to avoid, or even significantly reduce, the tax hit you have to impose on everyone if you were to give everyone in the country a health plan that's the equivalent of the typical large-group employer health plan, with the same AV and the same reimbursement rates to providers.

It's always politically popular to portray your preferred policy path as having no actual costs to anyone. All the expenses get paid for by eliminating "waste, fraud and abuse." But that's usually not enough. It's not enough when Republicans want to slash Medicare budgets while claiming patient care won't suffer (because we'll just be cutting "waste, fraud and abuse"). And it's not going to be enough to pay for UHC without seriously whacking a bunch of providers and/or raising a lot of people's health care costs (taxes plus premiums) from what they are now.