The idea that the "market" will always cause the correct distribution of resources is a simplistic fallacy.
What makes the "free market" ideology so misleading is that most of the proponents are unaware of the assumptions behind it. To get markets to get to optimal solutions you have to assume the following:
1. Perfect competition in all product, factor, and financial markets, a.k.a. NO LARGE FIRMS.
2. No collusion among market participants, including no trade associations.
3. Perfect information in real time instantly available to all market participants.
4. Perfect knowledge by all market participants of the future with no uncertainty. The market participants must also be immortal.
5. The complete absence of all externalities, both positive and negative (i.e. social cost must equal private cost) in all markets.
This is not a representation of the real world. If people really believe in "market solutions" then they would not obsess on the ideal but would work toward solutions that address these failings and make markets work more like perfectly competitive models. Of course that would mean abandoning 99.44% of all conservative cant, but hey, they don't want to improve things, they just want a political issue.
Redistribution through taxes is like having an overall, publicly sanctioned referee for the economy. Building more coal fired power plants might be the most profitable thing to do in the short term, but taking a broader view for society, it is probably a dumb idea. Who's going to say no, unless there is a referee? Tax policy can move a society into more productive, sustainable, pro-social directions than would be the case if left to narrow self interest.
In the case of the federal government, taxes are a tool of fiscal policy (draining funds from the private sector) and a tool for social and economic policy (tax credits etc). Per se, taxes are not a form of regulation, but they are very important in creating quasi-markets. You can have a regulation, for example, banning mercury emissions in coal fired electric plants above a certain level. Energy producers who are below the emission standards will not change their behavior, no matter how easy it would be. Those who are over the limit do a cost-benefit analysis to determine if it is cheaper to reduce the emissions or pay the fine. Guess what? A lot of the times it's cheaper to pay the fine. But place a tax on the mercury discharge, or better yet issue a fixed number of mercury certificates equal to the goal (say a 50% reduction), and let a market determine who solves the problem and how. Some will buy the certificates, some will change their production methods to reduce mercury, and some will fund research into more cost effect ways to stop mercury emissions. My number two son is a PhD researcher in macromolecular engineering working for a major chemical company who was on that particular project. It shut down 30 days after EPA announced higher thresholds than the industry was anticipating.
One of the most important aspects of a succesful modern economy is having a functioning middle class. Statistically, those with a middle income tend to spend with the most beneficial effect. Their money goes into the community, to businesses that create employment. When there is a huge surplus of income, it can often lead to negative effects, such as the recent housing bubble, or stock market run-ups. Tax policy is a way to ensure a vibrant middle class.
Only if tax policy is intended to support a middle class! It's a value-neutral tool. Since the 80's it has mainly been used to concentrate corporate power in both manufacturing and financial sectors, promote international tax avoidance distorting trade, and redistribute massive amounts of income and wealth to the top 0.01% of households.
A flat tax would simply redistribute wealth upwards, in an economy where this is already a massive problem. The idea that the rich would then use this money in the most pro-social manner is absurd, if history has any meaning at all.
First, you are correct that there is no reason the wealthy would use increased resources in a way the rest of us would deem socially beneficial. There's a good study of charitable giving that makes that point, and the listing of Koch brothers' donations upthread backs it up. Poor and middle class citizens give most of their charitable donations to their church and charities they are familiar with (Red Cross, United Way, rescue missions, youth programs, etc) which support both the middle class itself and people truly in distress. Rich charitable contributions are mostly to medical research and cultural organizations such as the orchestra, ballet, opera, and so forth. PBS may push their cultural programs to entice larger fund raisers, but their true base of support is anchored by Big Bird.