I have been asked this question a few times:
“why would a pterosaur give up a functional skin-and-bones wing structure to evolve a different, feather-based structure with the same function”?
Here are some things to consider:
In the dinosaur to bird theory, it is said that the first feathers were for display and for insulation. If those answers make sense in the dino to bird theory, then they could be equally applied to the pterosaur situation.
Another answer is that the pterosaur’s long wing finger makes it difficult/dangerous for a pterosaur to fly in the trees. It would damage the bone and tear the membrane. Feathers on shorter wings made it possible to inhabit the forests.
Another answer is that the ability of the feathers to open up when elevating the wing, reducing drag, is an advantage over the skin membrane.
And additionally, even though we may wonder what value the pterosaur got from feathers, the fact is that the birds were successful and the pterosaurs went extinct. The feathered version must have had additional value.
The question about WHY pterosaurs would develop feathers is often teamed up with the point that pterosaurs were doing exceptionally well for millions of years. Why change?
But exactly the same argument can be made about dinosaurs who were doing exceptionally well for millions of years. Why would they change? Same question.