It occurs to me that the only thing keeping Starfleet from being really effective slavers is the moral code, which seems like a really really thin barrier

Free upkeep with replicators. Medicine that is basically magic. Advanced personal weaponry that can be used to enforce compliance. They could easily maintain a supply of forced labor to do anything they didn't feel like, and you have to figure there's a timeline where a culturally degenerating Starfleet realizes it.