If I'm not mistaken, this is similar to the Warren Buffet view of the economy: yeah, get the government out of the market where it makes sense, let the market do its work, but then whoever wins needs to share some of that with the poorest in our society.
I think this all revolves around what the person means by "free market" Some people think this is a "free-for-all" while in fact a free market is usually regulated to some fashion to make it free (by guaranteeing private property rights and tort law for contract enforcement, if nothing else) So free market definitely does not mean lack of government support/definition/intervention.
Taking, for instance, the health insurance industry in the U.S.. I'm in favor of the government defining simple levels of insurance coverage, say from A to F. A would be total coverage for anything that went wrong (including preventive care). F might be catastrophic care only, with the guarantee that life-saving measures do not bankrupt the family (even is some measures might be denied).
In this case, the government can and should intervene to create the open market. Currently policies are so obfuscated by legalese that consumers effectively have no choice. In details-rich markets, like lending, insurance, airline fares, etc, the government can make the market freer by simply providing _simple_ standard categories of service.
As far as direct intervention in social systems, such as education, I think most right-leaning libertarians such as myself would support those interventions that directly related to things the government absolutely had to do. Education falls into that category because the need of a national army requires a standard of education. Health care in general is a very tricky area. We're developing life-saving cures for our elderly that cost more than the person made during their working years. I find it very hard to believe people in a democracy are going to vote for their own early deaths, so as a practical matter some kind of political appeasement needs to be made with the public at large, free market or not. I'm still thinking this one through.
The danger is taking a complex system and oversimplifying whether on the "leave it alone and everything will be fine" side or the "hey, we can engineer this thing to do whatever we want" side. It's way too complex to work like political slogans want us to believe. I think we're in agreement on this point.
People game systems. It's odd that you mention Newton -- the idea that some combination of regulations/deregulations will engineer a better economy is why our tax code is currently incomprehensible. Perhaps it might work if we try it again for the 50 thousandth time?
It might be better to look at the economy like a chaotic system, with billions of independent agents all working randomly yet somehow creating a greater whole. The trick is a minimalist yet-changing set of constraints to allow the chaos to continue and be productive. Once you start trying to put it in a box, or choose special parameters, or try to understand or constrain the entire thing in some fashion that you can understand, you're kidding yourself.
My opinion only. I can tell you that history is littered with really smart people, governments, and political parties who thought they could understand/control economics. Sometimes people mistake what I'm saying for laissez-faire or free-market philosophies. It's not. It's simply acknowledging that the over-engineering of things we don't understand usually ends up in stagnation and corruption, not growth and opportunity.
We're in quite a mess now in the U.S. because politicians get elected promising more things than they can deliver. If you ask me, we started heading down this track once the federal government usurped the states back in the 1860s. There's no more sharing of power -- people slowly are figuring out that they can directly vote themselves whatever the government can borrow. No kind of market or tax policy is going to be able to get us out of this larger problem. That's the meta-issue.