^This. If I were to make an attempt to create an interior that fit the exterior, I'd probably use the TOS engineering room as an impulse engine room. Then I'd use Phase II and TMP to guide me in creating a space with a reactor and clear shafts extending towards the nacelles. It would probably be a redress of the impulse engineering set- remove the back "trapezoidal" wall and add the long "TMP" shaft that snaked along the secondary hull's upper spine to the pylons. A forced perspective set. I'd use TAS as a guide for the main reactor in the engineering room.
Maybe the impulse room would look more like the one level, early engine room and warp engineering would look like the later two level space.
And if I wanted to show someone entering warp engineering, I'd slap a sign saying "WARP ENGINEERING" on a door at the end of the straight corridor.
The fact something like this was not done is likely attributable not just to lack of time and money. Whatever time and money they had could either be spent on a second engineering space or on other unseen parts of the ship that might have roles wholly unrelated to engineering, to allow story ideas to be explored that otherwise could not.
Another reason? Confusion. The fact that the ship has propulsion systems for faster than light and slower than light and that one might be a fusion rocket while the other bends spacetime... cool for geeks but probably not of much use to telling stories meant to appeal to a mainstream audience.
However, if you want to speculate about whether there is an engine room in the saucer of an idealized Enterprise... of course there is. If there is an engine there an engine room is there as well. Can they control the warp drive from this impulse engineering room? Sure! Why not?