This idea is a bit more... contentious. I doubt that anyone in Congress would vote for this, unlike some of my other suggestions. However, this one has more merit than originally meets the eye, as it actually kills four birds with one stone.
First, it grapples with the problem of too big to fail. If a bank gets charged more and more of its income as taxes as it becomes larger, the equilibrium size of banks will be smaller. Banks would spin off some of their divisions, which usually increases shareholder and economic value in the process, as people who understand each aspect of the business better end up with more say in it. The only people who suffer are those at the very top, who don't get paid as well because they are now executives at smaller companies. The rate of increase of tax to asset size would determine the ideal size of banks, and that would have to be studied closely before putting this into effect.
Second, it forces banks who gain implicit government guarantees of bailouts, due to being so large, to pay for that guarantee. After the bailout, the country has both the problem of moral hazard and a competitive advantage for large banks. They can borrow more cheaply since the government will bail them out if they fail, and then they are encouraged to be more risky with it for the same reason. A progressive tax will make large banks less profitable and so will cancel out that competitive advantage, and encourage risk takers to go elsewhere so that they can keep more of their gains. This will make large banks much more secure.
Third, it controls leverage. Leverage was a major contributor to this crisis. First, it increases the size of an asset bubble, then when all the banks had to sell off all their assets at once, it caused at asset death spiral. As they sold more, prices went down, causing them to have to sell more, pushing the price down further, et cetera. With Morgan Stanley leveraged 32-1 at the beginning of the crisis, it could only take a 3% decrease in prices before becoming insolvent. This policy would control leverage because leverage increases assets, and as a bank became increasingly leveraged, tax rates would go up, increasing the cost of the next round of leverage and making it more and more unattractive very quickly. Controlling leverage is a very important part of preventing another crisis, and this policy would do it automatically, with the market determining the limit.
Finally, it has a counter-cyclical. This means that when the economy is hot, possibly overheating, it will cool it down, and when we are in a recession, it will provide a boost. It does this also through leverage. I have already explained how it slows leverage on the way up, but it also does the opposite on the way down. As asset prices decreased, the tax rate would down, making more leverage look more attractive. This new buying power would help buoy the market when prices were going down. Also, in would increase tax revenues during boom times and decrease them during recessions, providing a clear anticyclical effect, just like unemployment insurance, but without the hazard of encouraging people to stay unemployed.
All in all, this policy provides a whole range of positive effects, and is one that I would really love to see put into place. This policy by itself might be able to stave off another financial crisis if calibrated correctly.