I have an original Colt chrome-plated carrier without forward assist notches. It probably dates from 1965, and I bought it strictly because I wanted to replicate a very early AR-15. I can't think of any other good reason to have one, but different strokes for different folks.
Functionally, they are a greater risk than a standard, phosphated carrier. The US DoD wrote a memorandum in the late 1960's directing that no rifle should leave the ConUS with a chromed bolt or carrier, essentially restricting them to training. I have never heard an authoritative statement of why this decision was made, but, like Canuck223 states, it likely had to do with hydrogen embrittlement. High strength steels can suffer a very sharp drop in ductility if hydrogen diffuses into the metal, and conventional acid-bath chrome plating operations all generate hydrogen ions at the surface being plated. It is possible to do a bake out to remove the hydrogen, but it is an extra step, and I am not sure how many plating shops have enough experience with high-strength steels to even be aware of the necessity of it.
Reviews of chromed carriers made by Les Baer or Smith Enterprises have generally been positive. Reviews of those made by DPMS have generally been poor. Either way, I wouldn't bother with one unless you had decided you had a real reason to want one.