I think the reason is they can dissolve the metals impurities easily. Other reason is the functional groups like C=O, C-O C-OH etc. are attached to the surface of CNTs which help them to be used to decorate CNTs surface to make hybrid materials with metal nanoparticles or other functional groups.
The nitric acid/sulfuric acid mixture is an oxidizing mixture. So, nitrate in acidic media goes to lower oxidized states, and oxygen atoms are attached to carbon. This is the reason why you obatain from carboxylic to alcohol groups in the CNT after oxidation (nitro groups too).
After the oxidation took place, the new groups at the surface interact with water molecules and the CNTs are more dispersable in water. Water does not oxidize anything.