Everyone doesn't withdraw at the same time, it's called synchronization. Banks have been operating for centuries at far lower reserve rates. There have been banking collapses but no dollar collapses during that time. Between higher reserve requirements and the FDIC, a bank run on the scale of the one that caused the Great Depression is unlikely.
The fact that banks do not hold all deposits on hand is a known fact, and something you explicitly agree to when making a deposit. Half this forum seems to miss the fact that banks are private businesses with which you voluntarily deposit money. They even pay you to do it.