The Romulans were confined to a single star system in early ToS and didn't get warp drive until later. The neutral zone was just a bit of interstellar space around their system.
I must have missed that bit, I certainly don't remember it (not saying you're wrong, I just don't remember whatever dialog said that, and I did re-watch the 1st season episode about them fighting the Romulans about a year ago).
Anyway, there was a lot of bad stuff like that in TOS, and even in TNG too, apparently written by people who don't understand basic astrophysics. A war with a race without warp drive makes no sense at all; either the combatants will be completely mismatched (any race without warp drive will be no match at all for one with it), or it'll be impossible to have the war in the first place (if both combatants are confined to sublight speeds, unless perhaps they're in neighboring star systems but even then you're looking at decades to send your Navy to fight the enemy).
Remember also, in the 1st season of TOS, there was no Federation of Planets! They kept calling themselves "United Earth Ship Enterprise". They didn't invent the UFP until later, probably sometime in the 2nd season. They just completely glossed over that.
Even TNG wasn't immune to science problems. The whole idea of the "star drive" section and saucer separating was idiotic, because apparently the saucer section didn't have warp drive. Without warp drive, you're not going to get very far; it's basically like having a canoe in the middle of the Atlantic. I still remember the episode "Arsenal of Freedom" where they do a saucer separation for some dumb reason (I think it was something related to convenience, not any kind of emergency). Without warp drive, the saucer section isn't going to even get out of the star system, much less to some other star system dozens of light-years away. If it takes 4 *years* for light to get from here to Alpha Centaur, that means the fastest the saucer can go that distance is some fraction of that, probably at least a decade (plus they'll have relativistic distortion, depending on how close to c they manage to go).
The bottom line is: you really have to take some Star Trek stuff with a big grain of salt, and this especially goes for anything involving TOS and worst of all the 1st season of TOS. Their understanding of astrophysics on that show back then really wasn't that much better than "Lost in Space".