Banks have the approval of the governments and as time goes on and cryptocurrency gradually crawls to hit the mainstream, the banks will change and improve upon their service. Banks will be left with no choice than to integrate Blockchain and cryptocurrency in their services in order to fall within the trend.
Indeed, this is so. Over time, banks will be forced to provide services in the crypto currency, especially this will happen quickly after the legalization of the crypto currency by the states. However, most likely, banks will only provide services for the purchase, exchange and sale of crypto currency, other banking operations with cryptovoyta for them will be too risky because of the large price volatility of the crypto currency.
As for the technology blockchain, the banks never refused to use it. This is evidenced by the good acceptance by banks of the ripple coin, which is based on this technology.