I think its just that air in the tank is compressed with a lower humidity than the normal air we breath. Plus with all the air flowing through out mouth during the dive, instead of through our nose on land, it dries out the mouth and throat.
have seen some divers attaching a small humidifier thing to their reg (at the LP port at the 1st stage, before their 2nd stage LP hose). Never tried it as i'm a little concern on the hygiene side of such accessory.
Personally, i just drink plenty of water before the dive, and also after. Have tried sucking on strepsels/fishermenfriends on dive, but stopped after a few went straight down my throat. Now, if it becomes really really unbearable during the dive, i just gargle with seawater.