I understand that it could be familiarity but although Kaladin is "acting like a lighteyes" he still has never really accepted them. I think he has a connection to the spear because it is the weapon of a darkeyes solider regardless of rank and he still is a darkeyes. If he uses any other weapon, especially a sword, it would be like accepting being a lighteyes and being that he has always used the spear, he would hardly use other weapons and would be less proficient with them, and again the sword would be especially hard for him to use regularly.