The economy is an interconnected system. If the banking system failed, then no one would be able to make over-night loans. If no one can make over-night loans, then large companies can't get the necessary funds for them to keep their regular operations running. If that doesn't concern you, consider that one of the largest companies in the country is General Electric. In simple terms, a failure of the banking system means the lights won't stay on.
Andrew Ross Sorkin talks about this in "Too Big To Fail" (http://www.amazon.com/Too-Big-Fail-Washington-FinancialSyste...). When things were really bad in 2008, and people were wondering what investment bank was going to go next, there was very real fear that eventually the biggest, most stable banks such as Goldman Sachs would go under. After Goldman, the next institution wouldn't be a bank. It would be GE.
Andrew Ross Sorkin talks about this in "Too Big To Fail" (http://www.amazon.com/Too-Big-Fail-Washington-FinancialSyste...). When things were really bad in 2008, and people were wondering what investment bank was going to go next, there was very real fear that eventually the biggest, most stable banks such as Goldman Sachs would go under. After Goldman, the next institution wouldn't be a bank. It would be GE.