One of the issues with this is that while yes, you can get the people to become more skilled/educated, ultimately the jobs that take advantage of that skills and education are in cities, not in small towns or rural areas where so many of these people currently live. And that's probably not gonna change.
Now, you could say, "well that's fine, we can give them moving stipends or something" but a lot of people are reluctant to leave what they've known as homes for so long. Such a strategy essentially puts these areas into hospice mode. That's an uncomfortable thought for probably most Americans.
And moving public sector jobs, while it might work, is probably politically untenable in America; the areas that are dying are the same ones that are generally hostile to government.