Perhaps I'm just too close to it all, but that's not how it will play out. The transition will be far more complex than that and the federal government will not be able to manage everything, much less implement sophisticated cost containment strategies that due keep overall costs down.
Keep in mind that health plans run on an average of around 3-3.5% margin. So even if the middle men surrender that back to the market, a 3% reduction in premiums/costs/taxes doesn't do that much.
And on funding, all non-poors pay the same premiums for the most part. If you shift the funding model to taxes, now the people paying higher %s will bear a disproportionate share of the burden. And it will be politically difficult to raise taxes on the middle class, so a small percentage of us will be penalized even further. So it's not the clean shift you describe in your first paragraph.