Surely it can specially if government will start to acknowledge and accept bitcoin and crypto currency as a legal tender of digital money. This is the main point of why bitcoin was born and existed as to how I see it. It's goal is to replace the use of fiat money and make it more easier yet more secured transactions with merchants.
In a positive thoughts yes, bitcoin can be the future of banking but if negative news will frequently occurs then maybe this will postpone it. Let us hope that the coming years will be fruitful for cryptocurrencies.