> Why do they refuse to lend if it is profitable?

Good question.

Note I didn't say it is profitable for the banks to lend to those segments. I said those segments can be lent to profitably.

In order to profitably lend to customers who banks turn away (mostly those with a 'bad' credit history based on credit bureau data, or those with little/no data at the credit bureau), you need:

1) Effective credit underwriting (i.e. accurate models/processes to decide whether to accept a particular application, and how much to lend to that applicant at this time), and

2) Efficient processes of acquiring, onboarding and servicing customers.

When a bank lends 10k at 8% for 3 years to a low risk customer, they'll make over 1k in interest over the life of the loan. So they can afford to have inefficient operations/systems.

When you lend 500 to a customer who is likely to pay back, e.g. 600 over the next 6 months, there's only 100 in risk-adjusted margin there, to cover all your costs of underwriting the loan, following up on missed payments etc.