There MUST Be a Reason That This Solution Hasn't Been Tried

I mean, other than the OBVIOUS one - that the Federal Reserve system, like most of government, is hopelessly corrupt.

My solution is simple - if a bank gets bailed out from its own stupidity in making loans that cannot be repaid, the Fed should:

• Allow limits on the amount that larger holdings by DEPOSITERS will be 'insured' - after the statutory limit is hit, the next $ 200,000 is reimbursed at 75%, the next at 50%, and down to $0 reimbursement. That will encourage the growth of banks beyond the 'Bigs'.
• Stockholders will have to take their lumps, and get their money - if any - from what remains.
• Any bank that failed, but is still viable, will need to be broken up into smaller banks, which will have to be audited (and, presumably, put their more feckless employees on the chopping block). 

The bank's boards will be responsible for repaying some of the loss, should their tenure have coincided with reckless operation. Those on corporate boards are, in fact, legally liable for not exercising due diligence and permitting fiscally irresponsible acts.