While you may be paying more in taxes, the average American will in the end pay more for healthcare (as a combination of insurance and out of pocket expenses). That this goes to healthcare providers and private insurance companies does not matter much; it comes out of your paycheck either way. If you're really uncomfortable with paying taxes to the government, you can pick the German system (where public health insurance is handled by non-profit sickness funds) or the Swiss system (where health insurers are private companies, but get told by the government what they have to offer and how much they can charge for it; they make money from providing non-essential addon insurance). In the end, though, either is still equivalent to a single-payer system in practice.
A major reason for the higher efficiency is that a single-payer system (economically, a monopsomy) can negotiate much better prices; prices also tend to be much more transparent, whereas in the US American system, the actual costs are often obscured. This is because normal market forces tend to work poorly in an unregulated or loosely regulated healthcare and health insurance market (e.g., ask yourself how much are you willing to shop around or bargain with a doctor when your health or even life is on the line).
But the US has a certifiably insane system. The government spends more on healthcare per capita here than the government does in France. To be clear: that's excluding private spending.
Some of that is certainly driven by a higher GDP per capita, but it's still ridiculous even when accounting for that.
The vision that taxpayers support a system where everyone is granted access to next-to-free / affordable health care has a natural cost in certain areas.
Sure it's great when you're both poor and sick cause you get to be treated like everyone else, you get the day care for your kids, you get the MRI's, the cancer treatment, you're being taken care of at the ER etc.
But at the same time, everyone has to realize that this has a cost in terms of taxes. Taxes for companies, home buyers, CEOs, businesses, cigarettes and alcohol, gas, etc.
It's the old chasm between putting the emphasis on the individual or on the nation/country as a whole. America has traditionally favoured private/capital-oriented solutions so far for most of its services (postal services, health care, public transportation, part of its schools, water, electricity, Internet infrastructure, etc.) and was thus able to keep the burden of taxes lower for individuals.
If it were to move to a system where everyone pitches in for cheap state-driven services, the money would have to come from somewhere and it would be sure to somehow stifle economic growth in certain areas (see the economic situation of France or other countries where the involvement of the state is still strong).
TL;DR: The idea of cheap MRI is nice on paper (and I believe it to be awesome in practice), but there's no magic wand to make that happen, the money has to come from somewhere and it requires that a whole country accepts paying more to the state to get more at the other end, a paradigm shift that will be tough to swallow for the USA given its economic culture.