So what is the problem with this? Only that moral obligations cannot simply reduce to divine commands. Why? Because they have inconsistent properties. Obligations exist necessarily, are immutable and objective. Commands, on the other hand, exist contingently (if the agent issuing it enjoys libertarian freedom, then this point is all the more obvious), possibly change, and are subjective. No one can choose something to be right or wrong, but persons choose to issue commands and choose the content of those commands. Obligations are categorical imperatives; they give us an unconditional reason to act. On the other hand, if someone were to just not care about divine retribution, they'd have no persistent reason to obey divine commands. As such, if obligations were metaphysically identical to divine commands, then supposing their existence would involve supposing the reality of contradictions. And so any obligation would have to be both necessary and contingent, immutable and mutable, objective and subjective.
In fact, the only property that seems common between moral obligations and divine commands is that they're both normative, in other words they're both action guiding. But it's a pretty bad metaphysical theory that tries to identify two entities in virtue of them sharing just one property!
The divine command theorist might just say that their concept of an obligation and their concept of a divine command are not inconsistent in this way. That obligations are subjective, that divine commands are necessary, and so on. But then the divine command theorist is twisting the commonly held concepts of obligations and commands, and without a very good argument for why divine commands are necessary, or why obligations are subjective, the theory is a very very poor one. I'd dare say it's better to have no theory at all, than to prop up a really bad one.
I think this problem would persist no matter what natural property we tried to identify moral obligations with. Indeed, I cannot imagine any natural property that is sufficiently like a moral obligation that the two could be married in this way. Because of this, I think the best option for the ethical naturalist is to just not reduce moral properties to anything, but rather consider them sui generis. This shouldn't be a problem, though, there are a whole host of natural properties in many different areas of discourse that we may also want to see as sui generis: "organism" from biology, "force" from physics, "meaning" from linguistics, "intentionality" and "consciousness" from philosophy of mind, and so on.