From what I've been hearing, as you said, payday loans do have a very high interest rate of up to 572%. Of course, when I acquired my own Acura Visa, I had one that was on the market price, and it fluctuated up to 5%. It was insanely good, on my part, but that was a special. I've seen credit cards that have insane rates.
I would say that if a postal bank awarded a credit card, the interest rates should be more in the low competitive range, at least by a half of payday loans if not lower, due to the fact that payday loans are focused on mostly acquiring that interest rate back from people. They definitely think it's because they focus on the lower-income people that they can have high interest rates.