Agree that the challenge is in obtaining partnerships, but not every retailer needs full control of the shopping experience, especially on mobile. And that's the win - alleviating the need for every retailer to solve the same technical problem.
In the mobile world with mobile optimized apps those redirects don't work. So app developers want to make the payment experience feel like it's happening "within the app" Twitter, Facebook, Pinterest and others all then had to solve for the inventory + payments challenge. Defaulting to Stripe can be problematic if the retailer already has a different payment processor relationship in place. By solving for the inventory piece I suspect Stripe is hoping to help drive momentum around overcoming the processor objections.
Full disclosure I work at Spreedly where we help solve for the payment dilemma (not inventory) by allowing developers to work with a wide range of payment processors and/or affiliate API's.
re Payments/Processor: So that's where it gets interesting. We have constructed for Pinterest a full payment distribution infrastructure to send payment information securely to large retailers or their processors. This infrastructure will also be used by Relay. Doing so, we believe we bring a ton of value to the ecosystem. But I'm sure you agree with that given your focus!