Broadly, what I'd say the tax structure needs:
1. Restructure/replace social security. Already went on a rant about this.
2. Fund schools out of the state level, with limits on donations to school related things and a federally mandated maximum per-student funding difference between the lowest and highest funded schools. So like, the richest public K-12 school in the state should get no more than, arbitrarily, 50% more money per-student than the poorest public school in the state.
3. Alter our tax structure so that instead of focusing our taxes primarily on MOVING money, we focus more heavily on stagnant money. So: inheritance tax, corporate tax on profits AFTER expenditures and wages, heavily bracketed income tax thus targeting disposable income instead of necessary funds which will be spent anyway. Dividends should be taxed as income for the receiving party, investments should be taxed extraordinarily harshly in the short term and then little or none in the long term (I would be OK with a 100% tax on profits made in the first day of an investment; that way you can "undo" an accidental trade, but you can't day trade).
4. Coronary to the above, we should start minting a little money every year, beyond just replacing existing money. Minting money devalues all existing money, in exchange for more money in the government's pocket. It allows you to essentially tax money without knowing where it is. No offshore haven will hide your money from inflation. Meanwhile, the little guy, you and me? We don't hold money for very long. Small amounts of inflation don't matter to us as long as our pay keeps pace (which it won't, but that's its own issue that isn't about taxes or inflation, we were always going to lose buying power).
5. Property tax should go into the general city, state, or federal pools rather than into school districts. Property tax should be small but constant; in an ideal economy, holding property should be a loss, but using it for economic activity should be a gain. I don't think that balance is practically going to happen, but we should at least try. Additionally, there should be an arbitrary percentage value picked for rent. If the monthly rent for a property is below that arbitrary percentage of its overall value, you should be able to deduct the difference out of, at the very least, your property taxes. That way poor people don't *necessarily* have to foot the bill for property taxes on their apartments. And they get punished a little less when property values go up.
6. For big, nationally relevant companies like banks and auto companies, voluntary nationalization should be allowed via the selling of shares to the federal government. Then nationalization of majority share should be made a condition for major bailouts or generous bankruptcy proceedings. Especially if corrupt or criminal behavior was involved. Any company that doesn't play ball, gets chopped up into tiny bits in the bankruptcy proceedings, and every inch of their finances audited for criminal behavior. "Too big to fail" my ass. Private city subway systems were too big to fail too, that worked out fine didn't it? Anyway, while not actually a tax, the federal government can either have its national company pay dividends to shareholders (and thus have a new federal revenue alongside taxes, since the government is a shareholder), or simply resell the shares later when the company's situation has stabilized and take that money out of the national debt. This would allow the government to step in to prevent a depression like Obama did with the bailout, but still punish the people responsible, and be able to less painfully accept its losses.
Basically? What rich people want, more than anything, is to use money to make money. As long as they can do that, simply by having money they continue to have money. That is the exact opposite of society's interests. As long as someone can keep a large share of money permanently, their buying power will remain higher than everyone else's. The result: stagnation, lack of power for everyone else, and skewed production towards luxuries over necessities. Meanwhile, taxing money that was already going to be spent either way isn't particularly productive. Since it encourages people not to spend money. When people don't spend money, the overall value of the economy goes down, AND the tax money goes down, since it was based on the spending of money. Obviously moving money will still need to be taxed at least a little.
As long as invested money will slowly but surely be devalued, the only way to keep afloat is to work. Thus, all people will trend towards needing to work for a living. Obviously anyone with a lot of money will try to fight this. But you know... still a battle worth fighting even if complete victory is unlikely.
For all of this to work we need a powerful social safety net for the elderly. The long term saving of money is selfish, anti-social behavior. But as long as people need to pay for their own retirement, the glorification of personal savings will necessarily continue.