I ran a Scott thermoplastic bar for DH in 96-98, then used that bar normally for riding until 2003, replaced it with an answer hyperlite carbon and used that for years, now have an easton ec70 bar thats been fine for the last year.
Running carbon bars on my current roadie (3T) and am on my 3rd carbon road bike,1st one, a cannondale did break, but still bought 2 more.
Carbon is fine, sure it can break, but so far never broken a carbon bar, but have destroyed 2 aluminium ones (both due to hyper bar ends). You just have to make sure you install al the equipment carefully and keep checking for any scratches issues (although I never did, only found the frame crack when I was washing my bike). They'll take anything that a similar aluminium bar will take pretty much.