No, It does not happen because banks are fully secured eg: central bank etc. So there is no need of adopting BTC..
nobody is adopting btc because of they expect bank backs will boost btc, yes it might tarnish the amount of trust people invest in it, especially affecting the market negatively causing panic. Its volatile nature already scares people and knowing how sensitive the crypto market is, I don't know how things work out but I hope they will
