The better analogy would be a fixed-cost loan with variable installments based on your income- a much, much friendlier loan structure for consumers.

What makes payday loans unaffordable is their structure, more than their cost. In California, a typical payday loan goes like this:

1- You write me a $300 check and date it for two weeks from now (when you get paid)

2- I give you $250 in cash

3- Two weeks later, I cash the check

If you had to borrow $250, what are the chances that you have $300 left over on your next paycheck? Zero. So really, it's:

3^- You come back to the store and say "don't cash that check, I'll get hit with a $25 overdraft fee."

4- I say "ok, give me $50 and I'll move your due date back 2 weeks."

5- You say "phew, thank goodness!"

6- Two weeks later, goto 3*

So the one-time payment is what makes it horrible. Even if they charged 0% APR and all you had due was $250, you'd still be hosed. An installment loan, though, where you pay $50 every two weeks for N months is clearly better, as proven by step 4 here.

I don’t think this is the case. Payday loans compound interest, don’t they? You end up owing more money the longer you take to pay them off. With this, you only ever have to pay back the advance and fixed fee no matter how long it takes.