We are still ways to go before bitcoin can challenge the banking system. There are still a lot of adjustments needed to be done on the blockchain to compete with the banks.
Why should bitcoin compete with banks? Do we need an institution that gives loans in bitcoin, or do anyone wants to give his/her bitcoin to an institution for a longer time to gain interest (in bitcoin)? I think bitcoin should be firstly a kind of solution for digital cash (and secondly digital gold).
Why people use banks?
- Security
- Money transfer to abroad
- investments
- loans
the first 2 could be done easily with bitcoin. If you have a lot of cash, you put it in the bank, they save it for you. If you need to secure your funds (in bitcoin) you can use paper wallet and hardware wallet, no need for banks to save it.
People use banks (or WesternUnion and similar) to transfer cash to relatives in different countries (or not just to relatives, but to anybody). They need a system that solves this problem. Bitcoin can do it easily and securely, and (if there're not too much transactions in the mempool), it's cheaper.
What do you do if you want to buy something locally? You go to the shop, and buy something, you pay by cash. What do you do if you want to give money to your relatives or to someone else locally? You give them cash. No banks are involved in local transactions.
But what do you do if there is a distance between the two people? They cannot use cash, because of it's phisical existence. In these cases you need to involve banks.
But if you use bitcoin, you don't need banks, because of the nature of bitcoin, because it's digital, because it's accessible worldwide.
It's not a competition with banks, it's just solving problems without them. If you have digital cash, you don't need banks for digital cash transactions.
But if you want to apply for a loan, that's another story, and you cannot skip banks in that situation. If it was possible to give loans in bitcoin, then it would be a competition with banks.