The fallacy to your thinking is that you see that as a government function rather than a private sector function. The government cannot put money into one hand without taking it out of another. So you have a zero sum gain or even a negative if you make the giver less able to give. When the private sector redistributes income all parties benefit.
So ask yourself what creates economic growth: taking more and more from the haves who earned it making them less able or less motivated to generate more economic activity that provides permanent jobs for all or promoting more private sector enterprise and activity?
But see, I never said the government should put money into the hands of the less advantaged. I am talking about the government taking more money out of the hands of the less advantaged by raising their taxes, which is exactly what would happen under a flat tax system.
We always hear the Conservatives and their over lords, the uber rich and corporate interests, telling us that raising the marginal tax rate for people enjoying lavish incomes over $250,000 as unfair and detrimental to the economy. Well, consider someone making only one tenth of that $25,000 having 15% of their income confiscated at gunpoint (that's the operative phrase, isn't it?) What happens to their meager spending power then?
And ask yourself, are there more people making a quarter of a million a year or only $25,000? Which group, by shear force of numbers alone, is more capable of spending and stimulating the economy?