I agree they simplified payments, but I don't see how they improved this product over PayPal. Both decide almost instantly and don't require a bunch of documentation.
Probably hard to improve on that process, but it does look like they are just playing catch up in this small area of their business.
Their entire existence has been built on that. They look for the burr in the saddle. If PayPal had not been so incompetent with their API, Stripe probably wouldn't have had enough of an angle in the beginning to gain broad traction among developers.