The Fed may or may not realize it but it has created a two-tier banking system:
1. Tier 1: Systemically Important Banks. These are the "too big to fail" biggest banks. If you have money there, it's a true deposit. You can't lose it.
2. Tier 2: Everyone Else. If you have money there, it's not a true deposit. It's an unsecured loan to that bank. You can lose it in a bank failure.
Now tell me, why would anyone use Tier 2?