Let's face it, the I phone app for rhp is not very good. I never use the app anymore yet make all my moves by I phone when traveling. This involves a lot of double tapping the screen to make the board fill the screen, and scrolling the board over so that I can push the "submit move". In return for these inconveniences, I get all the functions of the regular site, can see my games when it is not my turn to move, see pieces taken, use analysis board, and have the board fill the whole screen.
I support your recommendations, and would like a good app that eliminates all that double tapping on the regular site. I see little point in having the app as it is. I wonder how many other I phone users are like me; tried the app and then went back to the regular site. It's a pity that the work that went into the app appears wasted as it is.
To me, the two biggest things missing on the iphone app are the ability to create a new game (by challenge or rematch or accept open invite or enter tourney, etc...) and the ability to view an in-progress game when it's not my move.
And only because I don't like all the double-tapping if viewing the full web version, I still use the app, but I have simply resigned myself to the fact that I need to be on my computer to create a new game.
Iphone app rating 2/10. The 2 because the board is easier to view and use than the full version.