This is my opinion.Banks won't make you rich.saving in bank can never do that,because of interest rate that bank gives you is too tiny.You saving will be simply be eaten up by the sleepy monster called inflation. As a example I will take ,When I'm in grade school,each day I received 10Rs (my country currency) from my mother.It was enough to by me 2 meals,but in now 10Rs enough to buy 2 candies. 
Banks are just for keep your money safe! 
The purpose of the bank is not for making you rich, as you have said, the main purpose of it is to keep your money safe. The tiny interest that they give to people is there to serve a purpose, what purpose? To pursuade people to save in banks. What is the purpose of saving in banks? Well, it is not just for you but for the whole nation because when you save in banks, those money are being circulated and can be used as loans for farmers or businessman.The main purpose of banks for me is to have the money being circulated. If many people save money on their homes using coin banks,there will be a huge negative effect on the economy of a country. Banks are just for keep your money safe!