Stretch, creep, mechanical failure (from bending over the mast when it rotates), how to adjust it, stretching under load, stretch before the fibers in the core have aligned and a whole load of other issues have made acceptance slow on small boats. But the stays are heavy, so I think there is a gain to be made. It would also make it easier to build your own rigging without special tools. It should also make visual inspection of their condition easier.
UV degradation should not be too bad as long as there is a cover over the core. Cutting the stays by accident sounds like a freak occurrence. If you see it the other way, stays you can cut with a knife could be a safety measure.
You could under doubt accept fibre sidestays, but not a fibre forestay in earlier discussions <img src="http://www.catsailor.com/forums/images/graemlins/smile.gif" alt="" />