Yielding to a treaty port demand means Eminiar is giving up a major element of its sovereignty, allowing a foreign power to establish extraterritoriality ("we do just as we please here, your laws don't apply") and to operate military hardware from former Eminian turf to its own strategic ends. Or at least this is what the concept means today. Unless we assume a futuristic redefinition, it's difficult to see how Anan 7 could sign an agreement, unless Federation pressure really was so overwhelming it overrode Anan 7's concerns about being accused of treason.
Sure, there could be compensations. But "mutually beneficial" would still be but a pretty wording for the beginning of Eminiar's slow slide from a sovereign power to a vassal state.
It does pique my interest whether the disappearances were due to the local war, or merely something external that a forward base of operations (be it a forced treaty port or a friendly haven) would alleviate. If the Eminian system is a lone rock of safety in an extensive space wilderness, it would make sense for shipping to seek refuge there (either because threatened by this external force X, or simply for the universal lure of civilization), and thus fall victim to the local madness.
OTOH, Eminiar could be isolated from the wider galactic civilization not by distance but rather by this factor X, which is why no Kirk before ours came and forced them to quit their idiocy: it took an altruist and
powerful organization (UFP/Starfleet) to start caring about the problem of factor X when the default solution would simply be not to go to this dangerous place.
I agree that the computers waging the war might well have targeted visiting spacecraft specifically, either in a strategic gambit to put the opposition to a difficult position, or then rather because they wanted to maintain status quo and stop outsiders from interfering. But there's one thing to consider: when computers wage war against each other, surely things would spiral out of control very fast, and escalate to literally inhuman levels where sneakiness and ruthlessness much beyond the firing of the occasional tricobolt warhead would be the norm? That the fighting is as "humane" as we see, not that different from how humans would do it, indicates that there are safeties and limiters in place - to keep the computers from switching from Eminiar vs. Vendikar mode to pure computer vs. computer mode, a switch that would both escalate the conflict and
shift its focus away from the humans, whom the original arrangement was designed to intimidate. The balance of terror is maintained only if humans remain at the focus; otherwise, it soon becomes united humans vs. computers, and unity is what the arrangement was designed to prevent. Clearly, neither Eminiar nor Vendikar would agree to the war ending in something else than their respective victories!