Houses burn down a lot more frequently than banks fail. Also, I'll bet the odds that FDIC will insure the loss of money in a bank is much higher than the odds of a homeowner's policy believing a huge pile of cash burned up in your house AND even then your policy probably wouldn't have coverage limits high enough to reimburse you for substantial cash losses.
Oh yeah, then there is theft, floods,etc.
The biggest danger is that routine inflation will eat up that money faster than the rats in the basement.
Now, having some cash for a small emergency on hand isn't a terrible idea, but using your closet as a personal bank doesn't seem very smart.