Very good point. The possibility of a bank run makes it almost impossible to invest in any of those smaller banks without very specific focus on that field of Investment in my opinion. In addition it should be good for larger banks which can cheaply consolidate.
Imo this form of instability is quite sad, as good businesses like first republic bank could fail overnight just being destroyed by self fulfilling prophecies.
Maybe regulators even need to think about providing more liquidity security to smaller banks as in the current age large withdrawals can happen online within minutes and rumors are spreading faster than ever via social media.