As I completed my fourth day of cross-country skiing last Saturday, with several bruises resulting from falls going downhill as I was barely able to control myself, I was curious: Why don't cross-country skis have edges? I can't think of any downside to them, as far as I am aware, they would only enhance control going downhill. Please enlighten me if I am missing something.
Many cross country skis do have metal edges – I've owned many such skis. They tend to be backcountry XC skis though, not trail skis. Newer backcountry skis are fat and often practically indistinguishable from downhill skis other than for the bindings, but metal edges skinny skis used to be quite common.
For groomed trails or relatively flat, low-angle skiing, metal edges add unnecessary weight and provide little advantage. For more difficult trails and backcountry skiing, they're very useful to have.