There is no reason for it to give you 3 AIP a shot. 3 AIP is not worth killing any ship.
It's a very durable golem, in a fight it's very hard to kill it, but it has no killing power except for one-shot kills. Maybe I'm using it wrong (I probably am), but it can't survive an orbital mass driver, so homeworld attacks aren't useful, and I can't imagine any other target besides maybe forcefields that would be worth 3 AIP to shoot at.
So... if the AIP gain on health regeneration were either severely mitigated (maybe gain 1 AIP every 750k hp regen, so that the initial investment is small but continued use is self-destructive), or completely removed (not recommended, since the cursed golem has HUGE lasting power, and I can use it to tank entire planets, although I'm rushed due to the health depreciation), it'd be a worthy investment.
As it stands right now, though, golems can't be thought of in terms of the end-game. Homeworlds almost invariably have an orbital mass driver which just wrecks any golem except maybe an artillery golem. Golems are a mid-game tool that you invest in from the early-game, but you invest a lot more than a nuke. From what I've read, and of my opinion, it seems like golems should be used to crack those really difficult planets (or, for the powerful but high AIP ones, several planets), sort of like a nuke but with additional bonuses and costs.
Correct me if I'm wrong about any of this (which I probably am).