This was marked "insightful?"
Look, all this boils down to the multiplier effect: when an entity (such as the government or a local municipality or a company factory) takes in money (either through taxes or through selling a product), they then spend that money on goods and services in a particular area, which then is taken in by others, spent by others, etc., etc., etc. This creates a form of multiplier effect, whereby a dollar of activity by an entity causes a ripple effect in the overall economy that is greater than that dollar spent. It's why an entire town with millions in economic activity can evolve around a factory which only employs a fraction of the people in that town; the rest provides goods and services to the factory and to the workers there, and to those who support the factory and so forth.
(As an aside, your example about cutting taxes saving someone $200 but then they don't get $800 from the government--(a) government wealth redistribution is macro-economically neutral: as long as someone has $800 to spend, that will create $800 worth of activity--and it doesn't matter if that $800 is spent on food or as a down payment on a luxury yacht. And (b) your statement "Because for most Americans, cutting taxes means less money in their pockets. Not more." assumes a zero-sum game, which wealth creation certainly is not.)
So the real question is not "how can we spread the wealth around." This may matter if we assume wealth is a zero-sum game (but if it were we'd all still be living in caves), and it may matter if we want to help the destitute and the hungry, but from a macro-economic perspective it just doesn't matter. No, the real question is "what is the government's multiplier effect verses private industry?"
Meaning if we take a dollar from a corporation and gave it to the government, will that dollar turn into more dollars or less than if we had left it with the corporation?
Now if we left it with the corporation, the corporation could spend that dollar on investing in new hardware for their plant, or in paying salaries to their workers, or paying dividends, or saving the dollar, or giving that dollar to some rich CEO who could then spend it buying a bigger Mercedes Benz. WIth the exception of saving that dollar, the dollars kept by a corporation generally will go out on goods and services--even if that good is the rich guy's big ass car. But then, even if that dollar is spent on a car, it will then eventually go to buying more factory equipment or spending it on the guy who hand-tooled the leather seats, employing his leather-making craft long after the market for horse saddles has disappeared.
Point is, don't discount the idea that leaving the dollar with some corporation wouldn't have a net positive public good.
The fundamental argument over taxes between the right and the left basically boils down to who, right now, has the larger multiplier effect. President Obama is on record claiming the government has a net multiplier for government purchases of 1.57 (that is, for every dollar the government spends, $1.57 is added to the GDP), and the tax multiplier is 0.99 (that is, for every dollar the government taxes, the GDP is lowered by $0.99.) There are those who believe that these multipliers are wrong; otherwise, the right thing for the government to do right now is to raise your taxes 30% and spend it on whatever.
Other researchers suggest that the real tax multiplier is much larger: for every $1 in taxes, GDP is actually lowered by $3. That's because when the corporation doesn't have $1, that's $1 less net profits they have. That's $1 less they can spend on equipment or on salaries or on that Mercedes, which is $1 less their suppliers have; even the guy making leather seats by employing his ancient craft of horse saddle making has $1 less due to fewer Mercedes being sold to fat cats.
(source), follow the links to originals.
And sure, that $1 is a dollar that could be given to some poor person to buy food, clothing and shelter, which makes it's hands back into some agribusiness exec or clothing manufacturer or landlord's pocket to eventually buy a Mercedes for their own. But part of that $1 goes into the hands of a bureaucrat--so the poor person really only gets some small fraction of the $1. And because that $1 was pulled from a corporation, it's less likely to be spent on making a more efficient factory that can make cheaper goods, and more likely to be spent on making a more inefficient government bureaucracy. Remember: corporations (who aren't rent seeking by petitioning the government) has a vested interest in survival by becoming more efficient; bureaucracies have a vested interest in survival by becoming more entrenched through inefficiency.
That's the real debate right now; does raising taxes raise revenue, or does raising taxes actually lower revenue? And should the government further stimulate the economy by getting out of the way or by taking a more controlling hand?
Sadly what should be a technical discussion complete with phrases such as "multipliers" and "moral hazard" and "undue regulatory burdens" and "fiscal stimulus" has turned into a partisan fight using such phrases as "tea bagger" and " socialist" and "doody-heads."