While I'm sure we all support the notion that there is social good in reducing income inequality in the U.S. and improving quality of life for all, consumers in lower tax brackets will tend to spend additional income on staples, marginal quality-of-life improvements and servicing past debt. While this spending (increased aggregate demand) can't be bad, it doesn't necessarily distribute the capital _efficiently_.
Meanwhile, as you put, the high earners who "save" (read: invest) their excess income are precisely those who stimulate the economy effectively, as they are typically more able to efficiently allocate investments. I make this broad-brush assumption based on personal experience and some research I read years ago I don't have the time to look up right now. But basically think about this: if you had $100 to invest, would you rather ask a hobo on the street or Bill Gates (let alone Ray Dalio)? This "sophistication factor" is relevant, I believe. Add in the fact that lower-income consumers are almost certain to spend the excess capital in a predictable but not necessarily efficient way, and it's fairly easy to make the argument that aggregate demand would best be created by a.) efficiently distributing capital to b.) create new and profitable enterprises that c.) create demand both domestically and internationally, and d.) purchases are made (demand is created) for those innovative new products/services using e.) the money earned by workers paid by the companies that just created them. (f. what a mouthful.)
Now we've not only increased demand but added to the whole pie via foreign trade. And gets us back to the point mentioned above that the quality of what we create directly impacts demand for it -- and you can't really get around that fact either.
Gates and the Hobo have the same ability to spend (ie demand) with the money you give them, but Bill Gates and the Hobo do not have the same ability to produce. That is why Gates is Gates and the Hobo is the Hobo. It is the fact that Gates has a propensity and skill to take the $100 and create value (production) from it that gives Gates the ability to grow the pie for everyone.
Everyone - and I do mean everyone - would be better off if the fed government (and state and local) invested those tax dollars smarter by leaving the majority of them in the hands of those that earnt them.
"There are four ways in which you can spend money. You can spend your own money on yourself. When you do that, why then you really watch out what you’re doing, and you try to get the most for your money. Then you can spend your own money on somebody else. For example, I buy a birthday present for someone. Well, then I’m not so careful about the content of the present, but I’m very careful about the cost. Then, I can spend somebody else’s money on myself. And if I spend somebody else’s money on myself, then I’m sure going to have a good lunch! Finally, I can spend somebody else’s money on somebody else. And if I spend somebody else’s money on somebody else, I’m not concerned about how much it is, and I’m not concerned about what I get. And that’s government. And that’s close to 40% of our national income.” - Milton Friedman