There is no any monopoly over currency exchange. You can go in a bank and exchange your money by bank's prices or can go in a street exchanger and exchange there. The world is too far from the bank's monopoly, baddy 
Street exchangers work for banks or are owned by banks.
You don't exchange anything without banks being involved.
Cashless society is a banker monopoly, and a bad idea.
You make a few false assumptions in your post
First, banks and large international corporations are essentially the same. Some corporations even set up their own banks (though the connection may be not open, of course), so they can't possibly steal their own money. Further, you erroneously assume that the wealth of both big and small corporations consists in money they keep in banks. This is obviously not so. Even the largest corporations may have a very small amount of money in their bank accounts, just enough for current operational expenses. And if these expenses are small it doesn't make sense to keep plenty of money in the bank account
Almost anyone living in a capitalist country can start a corporation.
When it comes to banks, no one is allowed to start a bank. In many cases its illegal to start a bank, just like its illegal for someone to print their own currency. This idea you have that corporations set up their own banks has no basis that I have seen. Some corporations like facebook have their own digital currency that they allow people to use to exchange things. But they do not setup their own banking or financial entities.
As undoubtedly many have said before, banks have the best financial network for exploiting tax loopholes. All of those offshore accounts corporations and evil dictators use to hide money are run by the banking institution. This is a part of how banks wield so much political influence over politicans and leaders of the world.