I gotta say I was infuriated until I read your comment, you totally nailed it.

Distributing binary code to thousands of iOS users is dangerous, if nothing else. So Apple clearly has a point trying to control distribution through the app store.

And if the author truly does believe in curing sleep issues, as they state, then they should have released the source code and let people install the app themselves.

In fact, with 176000 page views, and 15 million downloads of their desktop app (I myself have been a long time user) I don't see why he didn't just pay the 99 USD and distribute it via the app store. I certainly would have payed for it because it pains me to see my SO in bed solving sudoku with a flipping 50W lamp in her face.