If health insurance companies are the problem, why are administrative expenses --- which we overspend on, to be sure --- not the dominant factor in our health care expenses? They aren't; they're not even in the top 3.

If Medicare managed all of US health care and nothing else changed (that is, if we relied on Medicare for funding and kept the rest of the system we had intact), we'd reduce prices by something in the low teens percentage points. Families upset about the cost to insure their families on the ACA markets would not be mollified by that level of price relief.