Besides the various possible changes to inherited wealth, how does one approach the problem of inherited knowledge about what is the right thing to do? In the Horatio Alger example cited above, the rich guy teaches the poor kid how to dress. In modern society, who teaches the low income parent how to dress? How to buy nutritious food. How to not have more kids than can be fed? (See above also!)

Suppose someone from a poor family gets into Harvard or Oxford (or French/German/Spanish equivalent), but doesn't know how to hold his fork correctly, or wear makeup correctly. How is society to fix this problem?

I believe that in the good old days organizations like the BBC and CBS made an effort to use their nationally received version of English pronunciation, for example, so at least in theory a kid from Wales or the East End or Mississippi or Yonkers would have an example of how to talk "properly." But now we have traded that in for more realistic entertainment, taking away this one small example of support for upward mobility...