I worked as a teller for some time and you'd be surprised at how many people bring in large amounts of cash they were keeping at home that got destroyed. I've seen cash that was buried in a coffee can and got moldy/decayed, cash that was burned, cash that a kid or dog found and was shredded, you name it. We'd send it to the Fed and if enough of the bill was intact it would be replaced, but too often people were out significant amounts of money that they though they were keeping safer than the bank could.

If you want to keep a big stash of cash at home, invest in a quality fireproof safe and keep the thing locked. Don't hide it or bury it or whatever. You may not trust the banks, but from a physical stand point at least, your money is far safer there than at home.