As you might have been able to tell, I build my rods almost exclusively with carbon grips, either with an epoxy topcoat or without.
There is a couple of reasons as to why that is.
Reason number 1:
Carbon grips enhance the sensitivity of a finished rod.
Both cork and foam type grips are soft(ish), meaning that they are essentially a massive dampener/cushion on your rod.
Because the fact that they are soft, they absorb a lot of the vibrations transmitted though the blank, making your rod less sensitive overall.
Carbon grips however are very hard and because of that, they transmit all the vibrations that come through blank, directly through the handle too!
This makes the handle section just as sensitive as the blank, thus maximising the overall sensitivity of the rod.
Reason number 2:
Carbon grips (both coated with epoxy or without epoxy), are far more durable than cork of any type of foam.
Being that carbon is a composite, it takes much longer to degrade. 
As a matter of fact, they figured out that these types of carbon grips take over 3000 years to degrade, so the rod will outlast the user.
Carbon grips are far less likely to scratch or damage, than cork of foam type grip would.
The uncoated grips have a hard carbon outersleeve and the coated carbon grips have 3 to 6 layers of epoxy, protecting the carbon making them even more dureable.
* An added benifit to the epoxy coated carbon grips is that you if the grips have some scratches, that you can take a polishing compound and buff out most of the scratches/blemishes.
Leaving you with grips that look clean and shiny, just like the day you bought the rod.
The carbon grips are also much easier to clean compared to other grips as the composite won’t adsorb dirt, water of fish slime etc.
So you just take a wet towel and wipe everything right off.
Reason number 3:
Carbon grips without an epoxy topcoat, weigh 30% less then cork or any foam type grip, for the same amount of volume.
Making the overal rod even lighter!
Epoxy coated carbon grips weigh approximally the same for the same amount of volume as “regular” cork or eva foam, but still have the positives that come with carbon grips.
Rubbercork/burlcork grips or high density foam grips like hypalon, are still much heavier for the same amount of volume compared to a coated carbon grip.
Reason number 4,5,6 and 7:
Feeling, grip, water and warmth.
Carbon grips…… 
provide a very solid feeling, where cork of foam type grips feels soft.
give the angler just as much, if not more grip both when dry or wet, than a cork or foam grips will.
don’t absorb any water making them much nicer to fish on a rainy day than a cork of foam grip that will absorb the water and stay wet for a long time.
will take on the temperature of your hand, keeping your hands warmer for longer in cold climates/temperatures.
Side note!
Epoxy coated carbon grips might looks slippery, but they are not, no matter if they are dry or wet.
It is just the glossy/shiny nature of epoxy that gives a slippery illusion, once you hold a coated carbon grip.
You’ll quickly realize that it is in fact, very grippy.