Stick shaking is already used for stalls, and only for stalls (ok, specifically, it activates right before a stall, but for all intents in this argument, that's the same thing).

Pilots are trained very thoroughly to react to stick shakers in one specific and immediate way -- execute the stall escape manoeuvre, and that's to immediately, with only very minimal instrument scanning (typically, just check altitude and airspeed), apply power and push nose down to the extent the surrounding terrain will allow you.

I do agree that dual input could be better handled, but I doubt we'll see many big leaps in that area until active side sticks become the norm. For Boeing aircraft with yokes, I can't see a good solution. Maybe have some kind of hard-to-miss, single-purpose visual indicator on the glare shield, like where Airbus puts theirs? Or an alert when the two control columns get unlinked?

Also, to be clear -- stick shakers are a Boeing-only feature. Airbus has an aural, but very distinctive "STALL, STALL" warning, plus flight envelope protection provided by the FBW system. Alpha floor protection (A.FLOOR) is the subsystem responsible for preventing stalls.