What do you think would improve by Stripe being in AWS? As a Stripe customer, I like the way Portal[0] allows me to outsource payments (almost) entirely. I don't see the advantage (relative to the cost) of building it into my product.
Hopefully getting Stripe's designers to take a crack at the AWS UI would be nice.
Resolving support issues is the only one I can think of. I have seen a non-trivial amount of Stripe integrators have to resort to social media, HN or reddit to get any real response to issues like Stripe holding their balance hostage.