At least in the EU, where Klarna originates and is headquartered, using AI as part of an automated decision making process would be illegal under GDPR.

'Payday loan companies' is quite a loaded term, generally used for companies with predatorially high interest rates (three-plus figure APRs). Klarna on the other hand is relatively competitive with a normal credit card, with rates of 20-30% APR typical.

I've never used Klarna myself, but I can see myself using it as part of a plan to buy expensive goods (furniture, white goods, etc.), and I don't think that there's any particular problem with it (from a consumer perspective) that makes it worse than a normal credit card.

Whether their business can support as many write-offs as it sounds like they make is ultimately not something I can comment on.