I don't think this would work very well. iPad typing, like normal typing, is all about muscle memory. Given a default position (fingertips hovering above middle row) each of my ten fingers has learned how to reach for and connect with each letter key. After reaching for a letter and tapping it my fingers immediately return to the default position. To type a capital letter I quickly tap shift with the pinky opposite the hand that will reach for that letter and then it's business as usual. Same goes for the symbol keys on the second page. This system minimizes the unique muscle movements needed to type the full spectrum of letters, numbers, and symbols. Sure: I'm making more key presses to type a single symbol in the current system, but many of those keystrokes are motions that I have learned to make very rapidly since they are used so often.
In this new scheme I'd be learning a new movement for each capitalization and special character. Seems like it will be a while before I'd become nearly as proficient as I am now (65wpm).
Also, adding flicks (especially downwards ones) to all of the keys seems like a recipe for wrist strain.
There are some interesting ideas in this post, and I'm not saying there isn't room for improvement on the iOS keyboards, but this isn't it. In the end I think it just boils down to needing practice.
And yes: I'm biased. My buddy and I buuilt an iOS typing trainer called TapTyping. We have seen people get some pretty impressive results: