This isn't really feasible. Bank executives will fill fight the regulations that stabilize their bank against market swings, and citizens will demand that the government do something when irresponsible bank executives lose their life savings. Banking regulations, like most regulations, are written in blood, but for some reason, the banking sector is the most adept at getting regulations overturned.
So the resulting system is a patchwork of solutions that force the government into the role of rescuer. It's just too difficult to get most regulations to stick long enough to prevent another banking crisis. Barring a Constitutional amendment to create a banking "tsar" with broad authority and who reports to no-one (i.e., non-political), the best solution we have is to have the government step in when banks inevitably fail.
So the resulting system is a patchwork of solutions that force the government into the role of rescuer. It's just too difficult to get most regulations to stick long enough to prevent another banking crisis. Barring a Constitutional amendment to create a banking "tsar" with broad authority and who reports to no-one (i.e., non-political), the best solution we have is to have the government step in when banks inevitably fail.