If your goal is truly to see fewer people living in harsh poverty conditions, an absolutely noble goal, let the free market be. Capitalism will (and has, see the extreme poverty figures) bring far more people out of poverty than any bureaucrat could ever hope to.
I don't believe progressive taxation is discriminatory. The more you earn, the more the marginal utility of each additional dollar you earn is reduced. Progressive taxation recognizes this, and therefore eases survival burdens on lower income workers - who are necessary for any capitalist economy to function - while continuing to allow higher earners to become wealthy. It's a good system.
Depends on what you mean by "work"--this is what things looked like in the late 1800s, early 1900s, in the US. Conditions for workers were bad enough that it led to the union movement, federal workplace regulation, etc.
For most people, you'd have a hard time saying it "worked", but for the handful of people who got rich during that time, sure, it "worked".
As far as growth being stronger with higher tax rates, I assume you're talking about post ww2 era? If so, then I think that was probably more to do with the fact that the rest of the world was destroyed rather than due to our tax code.
And it was a short lived thing, by the mid-late '50s things were sputtering, and the top tax rate was 91% ("We like Ike?"). JFK-LBJ reduced that to 77% (https://en.wikipedia.org/wiki/Revenue_Act_of_1964) to great economic effects (unfortunately, the increased tax revenues were not so much that LBJ couldn't do a guns and butter budget that almost bankrupted the nation, leading to a decade and a half of malaise).
Life is better with worker safety regulations, child labor regulations, overtime regulations, regulations on being fired (which we in the US generally don't have), and so on.
The goal of "let the free market be" is what made life brutal for scores of workers throughout the first part of the industrial revolution--we moved away from that all with good cause.
Very good point on commerce relative to raising the quality of life around the world.
I don't know why so many people give the state the benefit of the doubt when they mistrust corporations so much. I'm inclined to mistrust both, but at least a corporation has to compete to survive. The state has a monopoly, that's one of the reasons it is so dangerous. Never forget that most of the worst atrocities ever committed in human history were done by governments. Hitler was an elected official and all that.
The goal has got to be to keep as much power for the individual as possible. The is in part done by keeping the state out of most contacts between two parties.
Anyone can do this, too, and everyone should. Ultimately, anyone who relinquishes their political power this way gets what they deserve--to have others make their decisions for them.
I trust the state because I'm a part of it.
I have no specific reason to trust corporations, but I certainly don't trust any corporation that wants to engage in policy-making; that is something that should be reserved for the people, not business organizations.
They're both competing to survive, it's just that the incentive structures are slightly different. Corporations are trying to make as much profit as possible, and political parties are trying to get a majority of votes.
In theory, a democratic government should be more trusted to satisfy the desires of the people, because it doesn't weight those desires based on wealth. In practice, many democracies are dysfunctional which vastly weakens the incentive structure.