Thinking about undead, I came to the conclusion they would be in RL an equivalent of a perpetuum mobile, ie it somehow works forever, not intimidated by the laws of nature. Of course, this is fantasy, and is not bound to those laws. And I have seen somewhere rules, claiming that if undead don't kill (don't consume life force), they get weaker and gradually fall apart. Whatever.
To return to the golems... what if it is necessary to fuel them somehow? A common golem is 'run' with its spirit, that comes from somewhere, not important for now. The cheaper and faster created golems must be powered with something, maybe oil, but magic can do it too. Simply cast a spell to make it work again.
Hmmm... looks like it lost some part of the fun. But, it makes these golems need regular "power-ups", meaning plot hooks and potential weaknesses, raising somewhat their costs. Maybe the creator made them with this way, so they don't run forever, or become independent from the wizards help (both the golem and its owner). An option if anyone tries this.