There has been A LOT of discussion, debate/s, and arguments regarding CF wrapped barrels over the years but when you boil all the marketing BS off the top there is really only two benefits to a CF wrapped barrel.
They are lighter but, ONLY, when compared to an all steel barrel of the same diameter. You'll hear all kinds of stories about how they are stiffer or more rigid but that has been debunked many times and when you compare an all steel barrel of the same weight, which is usually about a #4 contour, as a CF wrapped barrel the all steel barrel is more rigid and has less deflection.
It really boils down to aesthetics. If you like how CF wrapped barrels look or you like the look of a larger contour but don't want the extra weight AND you don't mind spending nearly if not twice the amount for a barrel then a CF wrapped barrel may be for you.
But, if you talk to any of the barrel makers that will be honest with you they'll tell you there is a certain risk with turned down then CF wrapped barrel that it may not shoot as well as an all steel barrel. I've talked to one of the most highly regarded barrel companies out there that now offers CF wrapped barrels and they told me the only reason they offer CF barrels is because there is a market for them and they were getting endless calls to offer a CF wrapped barrels so they did. It certainly wasn't because they thought CF wrapping barrels makes them shoot better.
I have Proof Research CF barrels on my 6 and 6.5 Creedmoor and a new Christensen Arms Ridgeline 6.5 PRC which has CA's CF barrel. So far so good and they all shoot very well but that's a fairly small sample size and I know multiple gunsmiths that really don't like using CF barrels on builds because they don't trust them to shoot well on a regular basis. Some gunsmiths won't give you the same accuracy guarantee when you use a CF barrel.