Iron farms overpowered early game

I recently started a world where I built an iron farm before going mining. The ease of iron farms throws the early game balance out of whack. I think each zombie should only be able to have one iron golem spawned from it. (a single boolean nbt per zombie) This would mean iron farms would require a constant supply of zombies to work. This could be achieved pretty easily with a mob farm or zombie spawner, but both of those would still require doing some mining first for either exploration or supplies. This would help balance the early game experience without negatively impacting late game iron farms potential much.