According to WHO estimates [1], a quarter of Africans have goiters so I think it's safe to say that archaic humans suffered from chronic iodine deficiency.
Evolution works through reproduction so any condition that doesn't impact survival until sexual maturity is unlikely to face any evolutionary pressure. Since humans are tribal and took care of their offspring in group settings, survivability after procreation also has little effect.
[1] https://iris.who.int/bitstream/handle/10665/43010/9241592001...