Distribution seems like an easy problem to solve... App stores or software repositories. Am I missing something here? In 2015 all the major platforms have or the other other.
Turnaround for updates to a website is seconds, at most. Turnaround for updates to an third-party repository can be anywhere from weeks (Apple App Store) to years (Debian, RHEL, Ubuntu LTS, etc.). If you care about those platforms and you care about iterative deployment, web apps are so much better in that regard than native apps.
Of course, there are use cases where you don't care about those platforms or you don't care about iterative deployment. For, say, PuTTY, which releases roughly once every two years and primarily targets a single platform, these concerns don't apply and PuTTY in fact is a native app. But that's far from all use cases.
Exactly. For every web startup or established player, there's an equivalent native app running on a mobile phone, or also on the Desktop (from Facebook, and Twitter to Skype etc).
