Nothing at all; just as there isn’t anything stopping a mage from wearing full plate and fighting with a mace.
The difference is that a paladin isn’t just an armoured priest. Paladins are defined by their belonging to an order; The Silver Hand, The Vidicators, The Blood Knights, The Sun Walkers, and Rezan’s Chosen. Paladins by nature take an oath to serve The Light through the order they belong to, and follow said order’s tenets.
Priests, on the other hand, are spiritual casters. They exist in every society on Azeroth, whether they be Holy Light priests from Northshire, Elune priestesses, or Loa witch doctors. This is why every race used to have their own “priest racial”, to represent how each race worships a different form of divinity.
The reason there are no Void paladins is because it would cease to be a paladin; paladins serve an order to channel the Light (even when that Light is given via An’she or Rezan), as opposed to worshipping a plethora of deities like priests often do. Paladins and Light go hand in hand - once they stop using Light, they stop being paladins.
EDIT: Worth remembering WoW was heavily based on DnD. In DnD, the line between a paladin and a cleric was that a paladin serves an Order, whilst a cleric directly serve a God. This is why the distinction between paladins and priests in lore is the fact every paladin race introduced has also has an associated Order added with them.