Shouldn't you also have a third button to list available actions, or would you throw that away? Overloading the select button would be just as confusing; I hope you don't want to do that.
You're right of course. At some point a trade off has to be made among usability, discover-ability, and simplicity. (Pick any two).
Adding another button reduces simplicity, but enhances the other two. Apple's one-button mouse—at the other extreme—makes things simple and discoverable, but often not as useable as I'd like. I still don't know how OSX's equivalent to Windows' [Alt] key access to menu items (does it exist?)
I do think using three buttons are good -- I'm not so happy with the classic "Xerox Parc/Smalltalk" layout -- I'd prefer to have a button on the thumb (like many logitech mice have) and a scroll-wheel in the middle that's not a button.
Which leaves us with a bit of a problem for touch screens. While it might be ok to demand users to learn one and two-finger touch -- three finger touch might be going a bit too far...
I used to use an MX Revolution mouse[1] that had what you describe. Multiple thumb buttons, that amazing flywheel scroll wheel, that other thumb wheel. I loved that mouse.
Unfortunately I love trackballs more than mice now, and am severely limited in my choices. The Trackman is nice, and has a couple of extra buttons, but it would be so nice to have something close to what I had with that Revolution mouse.
In response to your comment above, no I wasn't being ironic :). I'm sure I've seen similar schemes before that informed my "idea", though.