Why traditional banks tend not to provide finance to the poor? As in title, quite a simple question - however looking for some more arguments and points of view. Mainly talking about the poor in developing countries, however if some arguments are more "applicable" to the poorer part of the society in already developed countries - would love to read them as well.
This is actually heavily studied question in development economics. Here are some common answers:


Lack of secure property rights in developing countries. More substantial loans require collateral, in many developing countries especially in rural areas people don’t have deeds of ownership for their houses or farms. Even when they have access to some deed the property rights might be not secure.
Lack of identification - this is related to the previous answer. In many developing countries it’s hard to prove that you are who you are. Again especially in rural areas people might not even have birth certificates. Hence, a bank who does not have local knowledge like loan shark might not get repaid because person just disappears. Hence the costs of private monitoring for classic bank are prohibitively expensive.
In some places it might still be physically very hard to reach the people or you can put it other way around people in many places can’t physically access banking services - due to lack of transport or internet.


Also I got these from the book Poor Economics by Banerjee and Duflo (recent Nobel prize winners) they go in their book into much greater detail of this issue, so I would recommend it and the papers cited therein for more info. Although the book deals with multiple issues so it’s not only about this - just mentioning it so you know what to expect if you plan to get it.