Its most fundamental flaw, surely, was that it taught the rich that it was in their own interest to look after the poor. When things got tighter the rich simply decided they could take it all for themselves - and let the devil take the hindmost. Any ideology which depends on the enlightened self-interest of the rich ignores the begger-my-neighbour attitudes of the majority.

I do not see Keynesianism emphatically teaching the rich to take care of the pour as own interest. If there was a progressive influence on the rich, it was more of neo-Darwinian flavor - the rich made the extra conscious conclusion that if you powerful, you have to use the power for yourself. Progressive politicians seem to believe in "invisible hand of self-interest" sincerely - just look at election campaigns, where the progressives expect the common quest to succeed while each taking care of yourself only; the conservatives (and the rich!) are much more cooperative among themselves (though it would be nice, of course, if they would believe in wider cooperations as well).

Any political system could be taken over by the rising power misbalance - running totalitarian within a democracy requires only an additional layer of monetary and media control; it is not much more fancy than running Windows on a Mac. Getting more power to divested classes is a good idea; but that cannot be settled on an automatic pilot; holding up the gentle power should be kept almost relentlessly. The idea that you can possibly do very little (if nothing) self-enforcing with power, and be happy with that, is very radical for these times. Keynesianism did not really play with that idea.

Not using education in modern times is akin to asking ancient humanoids not to use tools. Sadly, under the marketist revolution education degenerated to just another item of competitive advantage to be gained, or to be denied to others. Now, depressingly much of world's decisions (from political commitments to building yet another hotel or brothel over a gym or a library) are in the hands of elite power players and richer businessmen; they are not stupid, but increasingly rarely the brightest. The education systems of the rich, or of anyone else, could be more aware of the primate instincts of territoriality and pecking order. But teaching to subdue your ego, or to appreciate less greedy choices, is not a sin.