At my current program, subspecialty fellows institution wide can only moonlighting in their general specialty, not their subspecialty. So, for example, GI fellows can moonlight in general IM but not GI. That sort of makes sense to me if you consider that the fellowship might actually be needed in order to be competent at the subspecialty. Most subspecialties outside of psychiatry are going to emphasize procedures, including some that generalists never do. So yeah, I can see why you might not want someone who is, say, only halfway through their cardiothoracic surgery fellowship to be doing your heart surgery as a moonlighter.
But I don't see how this makes sense in psychiatry. Most of our subspecialties are more like "focus" areas rather than actual subspecialties that involve procedures or knowledge of a specific organ system. No offense to the child psychiatrists here but I think there is rather little risk to letting child fellows moonlight with kids, but hey, training is more about servitude than anything else, right?