Even more to the point, regardless of whether Eminiar really was a threat to shipping (no evidence on that other than as regards the Valiant, and she wasn't "shipping", she was poking her nose where no shipping should), the UFP government and its Starfleet did feel that Eminiar had to be forced to open a treaty port - and had given Kirk the mandate to do the forcing.
The mandate was explicit and specific to Eminiar, not something stemming from Kirk's standing orders. Kirk held no comparable mandate in "Bread and Circuses" where he responded to a surprise twist of events.
Kirk might have decided on his own that the Roman planet represented a threat to UFP interests. But generally he has not been entitled to act upon such decisions - precedent suggests that he would need to pick up an Ambassador carrying the authority of the UFP government before interfering with local affairs in any major way (or then invent a state of war to give himself added powers, "Errand of Mercy" style), and direct dialogue from "Bread and Circuses" further reinforces this.
Assuming the GO relates to actually sterilizing a planet, rather than bluffing about sterilizing a planet, that is.
Would going through with the threat have been warranted in "A Taste of Armageddon"? Kirk's mandate was not to eliminate Eminiar as a threat (we know of no interstellar reach for such a threat), but to get the locals to yield a treaty port. Yet by killing all Eminiars, the Federation would get its treaty port, a base for its vessels where local law did not apply and local rule had no potency - there would be no locals to contest the issue. Perhaps the stakes really were that high, which is why Kirk felt comfortable with making the threat.
Timo Saloniemi