A public bank, in contrast, does not have to put this absolute profit first, giving them the flexibility to enter markets where they might not be as successful, but they don't have nearly the competition for their services. Additionally, since this is operated by the state, they can benefit from business loans and interest as another form of revenue, giving them room to cut taxes or improve services.
EDIT: As consolidation creates both larger businesses and larger reserves of capital, this causes the bank to make more conservative loans. They must play more defensively. As these banks retreat from "riskier" markets, it leaves genuine demand behind. Look at the article's description of "predatory lending" near the top of the article.
Because there is this pent-up demand, a local bank could open a branch that captures some of that demand, and incentivizes locals with higher returns than the international bank because they can charge a higher interest rate. But the IntBank wouldn't still enter this market because the size is still too tiny to warrant their attention and/or the interest rates locally don't move the needle in their global reserves. It's literally too small to be worth the effort.
It's not a tragedy of the commons unless something artificially prevents banks from charging a profitable rate for loans. If no other bank is doing business there, and if any bank which does do business is allowed to make a profit, then certainly one will. Indeed, that's what the 'loan sharks' are doing: providing desired services at a market-clearing rate.
It seems to me that a public bank will end up having to be subsidised from the general fund to cover its losses, which in the case of American Samoa probably isn't very large.
It’s a whole lot of work to serve 55,000 people with a GDP of $13,000 per capita. There just isn’t enough economic activity to make this work from an international bank.
If it improves the local economic conditions by keeping money flowing in the local economy, then such a ban seems like a reasonable trade-off for the common good.
Being a greedy individualist, by focusing on chasing after marginally higher savings account interests rates, is likely going to be self-defeating in this case. Your dozens of dollars in extra interest payments are unlikely to compensate you for the other economic hardships you'll encounter because there's no local bank that will bother to make loans to your community.