I did just that when RBC started cranking up their monthly account fees.  My day to day banking is now at PC Financial (though I do not like their online system) and my future investments are now with Questrade (though I later found out that they charge a bit more than many other robo-advisors; however still half the bank).  

Banks are too greedy, their CEO's grossly over compensated and where and when I can avoid it I do.