It would be great if there was an actual Mathematica client for iPad, or if the iPad isn't powerful enough, maybe a Wolfram Cloud access interface app.
I agree -- the Wolfram player is OK, but at this point it would be great if I could just run and evaluate notebooks directly on the iPad. I just purchased the newest, 12.9" version, and it would be great to be able to use it in the classroom (i.e., to use demonstrations for students) with Mathematica on the fly. Mathematica online also seems very slow compared to what the Wolfram player can do (with its limited functionality).
News on this? The iPad Pro is already way more powerful than a lot of notebooks so it makes a lot of sense now to have a full version of Mathematica running locally instead of just the Wolfram Cloud app.
Read development plans in this direction in this blog post