A lot of fintechs don't issue credit cards today. Some have plans to.
If you hear them talk about the sorts of cards they will eventually release, what they want to incentivize is good behaviour on the part of their customers. Rather than getting more points for spending, maybe you'll get more points for paying off your balance on time. Maybe they want to give you the ability to create a single-use card when you're shopping online, and you don't have a history with the merchant and you're worried that maybe that merchant is going to compromise your credit card credentials.
In a lot of the discussions I've been lucky enough to listen to, I think the motivation for a lot of fintechs is to do better than what banks are doing today, because there's so much low-hanging fruit that hasn't been picked because for the longest time there have been barriers to entry.