Any Stripe employees want to comment on the idea of integrating this with a native iOS app via a web view? My guess is it will still be too clunky vs building your own, but the benefits of continued improvement may be worth it.
Does Apple allow that, without taking their 30%? I was under the impression that's why Amazon doesn't allow you to purchase books through the Kindle app anymore.
Stripe already works with several companies that accept payments and bypass Apple's cut, such as OrderAhead and Exec. There are some types of purchases that must go through Apple, however, such as digital goods/content.