If you take away payday loans with incredibly high fees and interest, it will get rid of some financial options. For some people, even a short term loan with crazy fees is better than the alternative(s) available to them. What do those people do? For example, lets say I have $5k in credit card debt, I incurred some unexpected cost and don't have the money to make the required payment (remember, these are people on the fringe, not financially stable ones). If I miss the payment, my interest rate skyrockets, and I end up paying a LOT more on that debt. If I get a payday loan, I pay a ridiculous fee (lets say I get a $200 loan with a $100 fee), but it's still overall better than missing the payment on the credit card. Without the "predatory" lending, that person is essentially screwed.
Also, the fees might be crazy high, but the risks of lending money to people on the fringe are extremely high as well. Many won't (or can't) pay back, so you have to factor that in.
The real problem isn't just the predatory lending, the real problem is that there are so many people caught in such bad situations that they don't have good options, to the point where predatory lending / payday lending places are either their only options or their best option.