In most games, I move with a mousetrackball, controlling everything with one hand didn't quite work out for me. I do use the thumbstick to navigate menus or the like, and it works well for that. As for the thumb button: I usually bind that to Jump, or to Esc (or whatever other key gets me to the game menu). It really depends on the game how much I use the thumb button.
If I were building a gamepad, I'd build something very close to the Azeron, but probably replace the thumb stick with a D-Pad, or 4 buttons or something along those lines. I'd put those to better use than the thumbstick. And I'd make the thumb button trigger by pressing downwards, rather than out.