It is extremely hard to get rid of the oligopoly and Visa and MasterCard make sure to keep their market position. My experience comes from trying to start a company in exactly what you are describing, using the OpenBanking APIs. So what I will say was just my experience and does not necessarily mean it is impossible.<p>1. Public APIs (I will be talking about the EU's public banking APIs following OpenBanking in the UK and PSD2 in Europe): if you think the public APIs will allow you to transact easily from one account to another, think again. In the EU a new concept called SCA (strong customer authentication) means that for every payment your user does, they will need to complete an SCA flow. These SCA flows involve a OTP sent via text, logging in to your online banking account to confirm the transaction, etc. Any form of SCA in itself is annoying and destroys the customer journey (imagine having to login to your online banking platform to confirm a payment every time you buy a coffee). However, what is more annoying is that banks control what sort of SCA they allow and since banks have a vested interest in other payment apps (that don't give them a cut) failing, they will make it as cumbersome as possible.
2. NFC Payment via Phone: even if you do end up solving the SCA problem, you will not be able to use the NFC capabilities on Apple's Core NFC platform. Why? Because Apple has decided that no financial application should be able to use the NFC capabilities because they are scared of a competitor to ApplePay (thanks Apple). As far as I know, you can use the Android NFC capabilities but don't quote me on that. Thus, you are stuck with QR codes, something western consumers tend to look down upon. Thus, that is your second barrier to creating a good solution on the consumer side.
3. Distribution: in order to distribute this, you must bring out new hardware. This is expensive to produce and integrating into merchant's POS systems is super expensive as well. Furthermore, merchants don't like having several payment devices standing around.<p>Long story short, merchants hate paying card fees. However, it is damn near impossible to build a solution that is convenient for the consumer who you are intending to convince, thus I do not see this Oligopoly being broken for a long time.