Carbon framed road bikes take some of the harshness of the road away, that alone would probably be my main reason for carbon since road bikes tend to have skinny, rock hard tyres.
It's not just about the frame being lighter and stiffer, to me that's a side issue that happens to be true.
I was quite surprised when I built up a carbon road bike, at how much better it was at absorbing bumps in the road, compared to the aluminium Triban 3 I had been using. That Triban 3 was better again than the really old Reynolds 531 bike I had used a few times, the thing was a complete boneshaker, albeit probably a very desirable bike... 50 years ago!
If a carbon frame is coupled with carbon handlebars, a lot of the road vibration is reduced dramatically while the frame itself dramatically reduces the harshness of the ride. One instance I will always remember on that carbon road bike was going over a bit of road rough enough to lift my rear wheel slightly and it made a "boing" noise.
When two cyclists get married, they should throw anodized cable crimps instead of confetti.