The short answer? Game theory.
The longer answer?
https://en.wikipedia.org/wiki/Volunteer%27s_dilemma
https://en.wikipedia.org/wiki/Free_rider_problem
And, more broadly:
I don't have a good answer for why this doesn't happen. However, the fact of the matter is that the wealthy, on the whole, don't naturally redistribute their wealth very effectively.
It doesn't work very well without broad participation.
Because keynesians don't really want to help the poor, they want to be taxed which serves as flogging to atone for their guilt for the poor, which then makes them feel better about themselves.
If we wanted to help the poor we would be making things easier for small businesses, not harder.
You don't help people by giving them fish, you help them by teaching them how to fish. I can't believe I'm having to remind HNers about this.
Edit: I'm with the others here replying with "reduced burdens on the middle class and small businesses" and "...teach a man to fish..." I keep seeing this basic income and wealth distribution topic on HN and I would genuinely like to understand why those preaching for these ideas never actually do anything about it. "Make the government bigger" isn't the answer as it'll then be used as a tool of oppression.
Further, assuming we implemented a basic income in the USA, how many generations until the motivators for innovation and advancing society are completely eliminated? I've everything I need at $BASIC_INCOME, and as soon as I start producing more income, the government is stripping it from me, so what's my motivation to ever do anything besides subsist on that minimum? And once everyone is just taking the minimum and not doing work, who's gonna farm the food? Drive the trucks? Operate a grocery? Build the houses?