Players have repeatedly demonstrated how wonderfully adept they are at abusing things that are large that can be repaired. When something has a ton of health, it is easy to never let it die because you have lots of warning. When being down to 10% health is still several million health, that's an issue. The player just retreats it, and then builds back up this superweapon... "for free" if they have a resource surplus.
From your viewpoint, we go from "there is simply no advantage in getting a golem, ever" to a situation where one golem equals, essentially, a doubled fleet cap. Think about it: if one golem is equal to your entire fleet, and can be repaired in the same manner as your fleet, then having a golem AND your fleet is a double fleet. That's game-breaking right there.
But... brainwave... your comment about mercenaries is interesting. If the resource costs of golems were waaay higher... hmm. Possibly if using a golem cost you 10x or more what it would cost you to maintain the entire rest of your fleet, that could work. The repair speed on them would also have to be really slow, so that they could only be used at full strength once every few hours. But then there could be a one-time initial AIP cost for reactivation, the existing high energy cost, and so forth. Golem costs could be adjusted to match their "fleet equivalency" in terms of their usefulness. So, some golems might be cheaper, as they are less useful, and others might be vastly more costly.
That would still make golems terribly expensive and inconvenient to use in the normal course of things, but it would make it so that people might actually use them. Hmmm, very interesting. That might actually be the solution I'd been looking for. Let me play with the numbers on them, and I'll see what that looks like.