Has this been tried before?
Actually, it has.
When Hobies were first introduced, the traveler system had that capability. However, the complexity involved proved to be unworkable (two traveler lines, two cleats and a traveler that wouldn't move under load). The "self tacking" system that's on the boats now (and used on nearly every beach cat today), has proven to be idiot proof and significantly faster.
Is there some reason this wouldn't work?
Depends on your definition of "work". Sure it will "work", but is it faster? No. Is it easy to use? No.
Sailboats going upwind are a balancing act - the sail's sideforce is countered by the lift generated by the hull (and boards - if the boat is so equipped). In order to generate lift, there has to be some sideslip. It's a very complex situation and just pulling the sail higher to weather has all sorts of unintended consequences - like increased sideslip.
The bottom line is that Hobies (and catamarans in general) do not respond well to weather sheeting the traveler.