You assume that the rich, if left untaxed, will use all that money to help the poor. However, history shows that instead they use their money to buy themselves cars, private jets...ect. Hence, investing in production of expensive things that dont distribute to the poor.
Why do you assume rich people are spending their money in cars, boats,etc. I see you dont know anything about being rich. Rich people are constantly investing their money in companies that most of the time don't work out, and a very low percentage of it is devoted to frivolities like traveling, sex company, gumbling, etc. It's imposible to spend all this money in this shit because it's too much and from the financial point of view it's very risky.
Lowering taxes for rich is actually desirable because they would have more money to invest. You know, money should always be flowing around the market since this is the only way to generate more returns, and the more returns there is, the more taxes the goverment can gather. It's a win-win game.