My issue with carbon bars isn't strength. They're plenty strong for any just short of being a beastly world champion track sprinter.
My issue is with the flexibility; it's what makes them great for things like Paris-Roubaix and other cobblestone or rough-road races. For singlespeeding around on all the hills that I do, I don't want power lost to flexing the bars when I pull on them for leverage. I'm not taking the time to look it up again, but one of the big bike mags did a handlebar flexibility comparison within the past year and for minimal weight differences, aluminum bars were far stiffer.

There is a high probability that I will still use an aluminum bar when I build my carbon distance bike.