Try making a rule. Something like, "Hey Joe, can you not draw on top of the combat? Can you reserve your drawings for your actions and turn? It is difficult for me to select tokens when you draw on top of them." and if the problematic behaviour continues no matter how much you request their attention instead of random side scribbling, kick the player out. In my group, we only draw if we are demarcating a spell effect, and delete our drawing once it gets GM approval. I think this is a very reasonable use of drawings, and would be a fair rule to set. I would also consider that if a player is drawing a lot, deactivating their ability to draw might impact their fun. They might be happiest in a game where they can doodle to support what they have to say due to how they think. Blocking their ability might be the thing that lies between them having fun and being bored, so it could just be an innate incompatibility. But... if they just want to draw, maybe they'd be happier doing a DnD webcomic or making marketplace assets or drawing portraits of the party members or a future battlemap. Maybe you can direct them to use their urge to draw in a constructive manner, something other than drawing on top of everyone else's game.
