Regardless of government policy (had there been no Reagan) America's (uniquely) one-sided labor market -- disappearing unions and naive and complacent American labor -- would have brought on catastrophic inequality anyway (so catastrophic, if you live under 50 percentile income, that "inequality" seems a weak, under-descriptive term).
Naive and complacent labor is the root of all American inequality (or great wage depression) -- lack of simple understanding of relentless labor market squeeze that has to be deliberately met. America -- having a much better labor history than Europe -- has not developed the same over-defensive labor ethic that Europe has developed. We instead have our pioneer cult of the self-reliant individual. Ironically this leads our labor force to NOT take care of itself in the market place but to just trust unseen forces to fairly set labor's price. The latter might be a good angle to sell properly taking care of themselves to Americans once they wake up to the prosperity they (uniquely) have been missing out on.
American's might wake up if their media ever gets around to informing them that a true poverty scale (not one made up of a multiple of cheap meals) might show 25% of Americans living below the poverty line -- up from 15% in LBJ's era; double the average income since. They might also wake up of the media ever informed them that 25% of our workforce is now earning less than LBJ's $9.90/hr minimum wage, ditto doubled income. The media itself might wake up if progressives ever make enough stink over these two all telling stats.