Ah! If you mean "giving poor people more opportunities, thus leading to better use of human capital, increasing everyone's living standards,"

Thank you for figuring out what I was thinking! One of my many problems in any discussion is I can't figure out which things I need to state because there are other interpretations and which things I can leave unstated because everyone will quickly read it the same way.

This is the one I mean. I am fascinated by the progress human kind has made so far. I am interested in bringing that to new levels, and one way to do that is to use the pool of human resources we have ever more efficiently. Getting rid of arbitrary limits on what women or black people were allowed to do has been a great help in that goal. Avoiding a debilitating stratification may also be important.

do you have anything in mind when you refer to things that are better than, say, a public education system at providing poor people new opportunities?

Having raised kids, it seems unlikely to me that institutionalized public education for a nominal 6 hours a day (two hours work in 6 hours?) is all that need be done. Meanwhile, we observe that the more money a family has, the more they spend on advantages for their children. So while inexpensive or free public education is one good approach, another is just making poor families relatively richer generally. Which is most efficient? That is a discussion I think we should have, and i don't think the answer is trivial, or that there is even necessarily only one "correct" answer. But the ideal that "we should all get to keep all the money we make, and spend it only on our children if we want" is a point I disagree with, and what I wanted to argue against in my OP.
The captains of industry are generally from families that have given their children EVERY advantage. Of course it may be far from optimum to try to get to equality of

So yes, education is a great component of the kind of redistribution that I want. I suspect a more intact family doing more "enriching" activities together, not living in relative squalor, being able to teach "healthy choices" because price is not the only consideration when acquiring food, these may make generally redistributive policies efficient. Add to that our clear knowledge that marginal utility of dollars declines as you get more dollars, and we have a straightforward reason to choose progressive taxation to fund these things. (Note progressive income tax is not the only way to tax progressively, and income tax would not be my first choice of taxing, but that is another discussion).