Of course you're describing exactly the system that the US has already. How clever of you.
Except you've omitted one tiny fact: the US system costs the US government (and thus US taxpayers) approximately 4 TIMES MORE per citizen than socialized systems, and the quality of care is demonstrably lower.
You don't do socialized medicine because it's kinder to poor people (although it is)
You don't do socialized medicine because it creates a healthier and more productive population (although it does)
You don't do socialized medicine because it removes the profit motive (i.e. denial of care) from the healthcare equation (although it helps to do this)
You do socialized medicine because it's cheaper.
Anyone who tells you that socialized medicine is more expensive, and/or will lead to a poorer standard of care, either works for a US insurance company, or is willfully ignoring all the evidence from every other industrialized 1st world country, or, like you I suspect, is just a fsckwit.