TCAS (the Rockwell Collins proprietary system which meets the ACAS standard) works on the basis that aircraft at different altitudes cannot collide. Aircraft on different headings can collide - depending on their relative positions. TCAS resolves the relative position of the target aircraft via radio direction finding, which simply isn't accurate enough to resolve the position of an aircraft to calculate an avoidance trajectory. (Watch a target aircraft jump around as it flies an ILS to see how rough the position finding is!)
Using an encoded GPS position via mode S transponder transmissions would require a new compulsory standard throughout the industry, and simply isn't necessary.