Plus, later episodes in the spinoffs (including the immediate TAS) reinforce this impression; there's even a star system inside
the actual Zone, between UFP and Romulan spaces, in "All Good Things.." - the Devron system, out of limits to both Picard and Tomalak until they mutually agree to ignore the peace treaty.
Whether this deviation from the apparent intent of "Balance of Terror" was a good dramatic choice is debatable. We can also argue whether it happened by design or by accident. But Romulan space covering lots of star systems is now a solid given. What is less clear is whether Romulus, Remus, Romii and the comet are at short (impulse) or long (warp) distance from the Federation space; they could simply represent the extreme edge of a vast star empire, with the big bulge of Romulan holdings pointing away from the Federation.
The one thing speaking against this latter model is the thickness of the Neutral Zone witnessed in the map of the original episode. If the thickness is to be uniform, then one grid square on the map must be enough to contain an entire star system at least, and wide enough to require at least one hour of travel at high warp by a modern Warbird in the TNG episode "The Enemy". If the thickness is not uniform, we require a pretty impressive explanation for this curious fact!
Then again, a stretch of border immediately adjacent to the Romulan home system might receive special treatment. Possibly this is akin to the inter-Korean border at Panmunjeom, with the otherwise quite broad border exclusion zone locally limited to a line on the floor of a guarded building.