Banking is not inherently problematic or corrupt. The problem comes when the state 1) ensures deposits, and 2) gives them a monopoly on the creation of debt-backed money. The bankers book accounting profits when they make risky bets that pay off. But when the deflationary bust follows the inflationary expansion, the deposit guarantees become become a hammer over the sovereign and/or central bank, who ultimately take the bad debts off the balance sheets of the banks giving them good money in return (e.g. Maiden Lane and MBS) because they don't have any way of making good on the deposit insurance if they let the bank fail. Thus, profits are privatized for the bankers' bonuses, and losses are socialized, either through debasement of currency or outright bailouts from the sovereign (e.g. TARP).  This corruption is not even an unintended consequence of statism. It's right there in the FDIC charter (in the US case): "to create confidence in the banking system". Why is it a good thing to have confidence in an insolvent bank?

Under laissez-faire capitalism, bankers would have to compete on the basis of solvency, and would live in mortal fear of a bank run. They would never have taken the risks they ran in the runup to the banking crisis. Depositors would understand that their deposits are no better than the ability of the bank to make good on them. Depositors would want to know that the bank is solvent.

But because the sovereign and central bank are backing the banks, the ultimate consequence (historically) is debasement of the currency in an attempt to preserve the status quo by covering bad debts of banks (as well as to cover the fiscal insanity of the sovereign who can always find voters willing to vote for free-anything that the state otherwise has no way of paying for).

That's where Bitcoin comes in and why it's different. It can serve as a monetary base that cannot be debased by the state. It is a currency that can't be hyperinflated away.