One of the many problems which this idea has is that it redistributes money away from people who are good at investing in growth, and gives it to people who are likely to spend on consumption goods.
...which is fine, really, because spending on consumption goods is the basis of the modern economy anyway. Giving money to the poor is one of the most effective ways to give money to the rich, and has the nice side effect of feeding a few mouths along the way.
Money invested in growth has different economic effects from money invested in consumption goods; the former is likely to be spent on capital goods, and thereby increase production and reduce prices in the future, whereas the latter is likely to be spent on raw materials and labor (or possibly just driving up prices), with fewer long-term benefits.
Your ignoring the most profitable use of capital which is bribes. Current tax laws are vary focused around letting rich people keep there money but there is little evidence US growth is particularly capital constrained. Overall economic growth tracks vary closely to population growth long term Per capita economic growth tending to hover around 1%.
Economics 101 is a vary limited model of how real world economy's work. In the real world ultra rich people tend to cause a lot of long term economic harm because there goals tend to be vary different from most people.
PS: Bill Gates sending aid money to developing areas may be a 'good' thing but it's not investing in the way your thinking.
Large corporations (such as those listed on the stock market) are not capital constrained, but the small, new and potential companies which are most important to growth are highly capital constrained.[1][2]
Some have argued that it is good that rich people often get their way, because the alternative is far worse.[3]
Small companies may be capital constrained, but the constraints come from friction more than from limitations on capital supply. If DD on the proposal for Joe's Diner is going to cost more than the pre-DD profit expectation, it doesn't matter how much capital is in the pool, Joe won't be getting funded.
There's a nifty way around this: if Joe self-funds, he need not worry about his own principal agent problem. What kind of economies encourage self-funding? Those that provide employment opportunities sufficient for the purposes of saving and serving as a safety-net. NOT economies that systematically de-leverage the bulk of the working population.
