I agree that this proposal would not solve all of the problems; absent more changes you would still see the creep up of healthcare costs at too high a rate. But slashing $1 trillion off of a $5.3 trillion costs is a pretty big bite of the apple. Even if you go with the more conservative $663 number, that is still a great first step. And both of those numbers are after adding the costs of covering currency uncovered people. So we are collectively getting more for significantly less money.
It does this by eliminating a very inefficient layer of our current system (insurance companies), and by having there replacement for that (the government) negotiate on drug prices (how much savings there is the reason there are two estimates). Currently insurance companies almost have a negative incentive to push down drug prices (their profits are limited to a percentage of total spending, and most large companies are pushing against that limit).
Most of the cost control pressures in our current system come out of Medicare/Medicade, and this would widen that out to the whole system. That in turn would wedge open the door to pushing on the other drivers of the cost spirals: hospital administration, new expensive drugs that are not worth the additional costs, doctor salaries ballooning, and the broken system between malpractice insurance and dysfunctional enforcement against malpractice.
I understand that theres an argument for removing private insurance companies in favor of thr government can cut costs. It can also increase them.
I'd argue that the primary issue with insurance costs today is the lack of market competition, obscurity of what costs and prices are, and government protections that prevent insurance companies from being legally liable for many of the problems they cause.
Corruption and monopolistic practices is a big deal in healthcare, for example. We'd be better off, in my opinion, by solving that rather than killing an entire private industry and hoping our government can continue to do it better indefinitely.