Precisely why I stopped using it myself. One way to mitigate the problem is to place flags or light sinks between the subject and background, but just out of frame. I will reduce some of the scatter that creates the fringing, but not eliminate it completely. Another thing to watch is the reflected light from the chromakey backgrounds bouncing off a light ceiling and other objects, creating a color cast that is not pretty.
I like the concept for knocking things out, but in actual practice, it has its problems. The only other suggestion if you want to keep using the background is to create a lot more separation from your subject, and not just having it placed behind them. In other words, place the subject a good 5-7 feet or more in front of the chromakey background, light the background with controlled light to prevent it blowing out too much, and shooting your subject with a longer lens to flatten the perspective a bit more. Sometimes that works.
LJ