Banks present a tempting target for taxation because that's where the money is. As with other forms of corporate taxation, though, who pays the tax to the government and who ultimately pays it can be two different things. This point is both so elementary and so important that if you hear somebody claim that the solution to raising more government revenue is to tax corporations rather than people, you can dismiss him as an ignoramus. Failing to understand it shows an inability to do what the economist Thomas Sowell calls "thinking beyond Step 1." Step 1 is the levying of the tax. The further steps, which involve thinking about what happens next, are what Sowell considers to be the essence of the economic way of thinking.
Somebody, literally some body, has to pay the tax. That somebody is a combination of the customers, employees, suppliers, and shareholders of the corporation. A tax on bank profits, for instance, reduces the amount that banks can pay to depositors, bank tellers, furniture makers who supply bank offices, shareholders, etc.
If you don't find the argument convincing, think about a tax on gasoline. The gasoline does not pay the tax because it is inanimate. Oil companies collect the tax, but the people who pay most of it are drivers, every time they fill up the tank. Or think about a property tax. As anyone who owns a house knows, the property itself does not pay the tax; the property owner does. If he rents out the property, it becomes a charge he tries to recover from renters.
There are only three logical reasons to tax corporations. One is that because of the way the tax code is written, some income that would otherwise be taxed as individual income escapes taxation by being sheltered by the corporate form. In that case, the best way to address the problem is to reform the tax code. The second reason to tax corporations is that it is more efficient, since there are many fewer corporations than there are individual taxpayers. Before the rise of the welfare state, this reason might have made sense. To generate the huge amounts of money necessary to run the welfare state, though, governments create tax collection agencies to keep tabs on the finances of millions of individuals. The final reason to tax corporations is to hide the effects from people who can't reason beyond Step 1. I think this is the dominant reason for taxing corporations, including banks.