[Mashimo]

> Never build your main business on somebody else's platform.

Are there any (profitable) phone apps that are not build on top of the app/play store?

[Crestwave]

They're distributed through the stores, but not built on top of them, as is evidenced by the fact that you can distribute the same app on both platforms.

Android also supports third party stores/standalone installers and iOS is fighting an ongoing legal battle due to its lack of a permanent equivalent.