if banks will handle bitcoins and other crypto currency it will make a lot of changes. first the legality of bitcoin and before that happen world bank will impose laws about it. then it will soon have physical body as money that can be use not just in online.
You mean at a printed bitcoin (coin or paper) ? That not happen. It is impossible, it wont work.
First if the banks will take over the bitcoin , his price will drop for good to 2000$ or to whatever is the real price because it's a cryptocurrency and by definition, a crypto currency is meant to be free/not controlled by an entity ( decentralized) and i bet most of the bitcoin owners are not happy with this idea , the bitcoin is a deflationary store of value much better than precious metals.The bitcoin owners will sell it and move to a really free/democratic cryptocurrency .
It is very much likely that people won't declare all the bitcoin paper money if those are made illegal. Also once the bank knows how much bitcoin paper money you own, it is very likely that a tax might apply so again people wont be happy with this idea.
Second ,there is a cap limit for bitcoin, 21 millions units . This mean it can't be printed over and over like the fiat money . And the banks never know in real how many papers or coins of bitcoins are lost or destroyed to print again ,but to keep the 21 millions cap in circulation. Unless banks will call all the bitcoin owners to the bank with their bitcoin paper money to prove how many they own so the banks can make a real statistic about how much needs to be printed again.
I guess you know, from time to time, central banks are needed to print money because the money can be lost, destroyed, used, etc. How can money get destroyed or lost ? Well imagine a millionaire house is burning and that millionaire has bitcoin paper money which are burning too. Or imagine a car accident and someone has an important amount of bitcoin money with him in a suitcase but the car jumps into a river and no one will know about this. So every year fiat money are lost ,destroyed, etc. and the banks have to print periodically paper money but with bitcoin is impossible to know how much needs to be printed again due to its nature, cap limit to 21 millions units.
Banks will prefer to create their own cryptocurrency (deflationary instrument) so they can control it 100%, without making it a paper print too, they will know anytime how much is their reserve in cryptocurrency.
Gold is deflationary but not to much. Internal cryptocurrency which im pretty sure its nothing special and it is most like dollar deposits .
The profit will come from investing it (buying stocks market for example) or from its increasing price vs dollar due to the trust/size/expansion of the bank, etc. Banks will always want your dollars so they will attract you with their cryptocurrency to buy it but basically it is nothing special, just an investment instrument or another way of depositing dollars .If that crypto currency gets printed on papers, banks will lose digital exact statistics and they will have to print every year new banknotes to keep a good amount in circulation.