I'll throw in another of my own tech notions from 20 years ago to further complicate the picture. I used to participate in a postal-mail-based fandom tech- and art-based roundtable back before the internet was available for the masses. (Imagine that!)
The rounded Federation nacelles on the TOS era (which fandom since labeled PB-32 "circumfirential" warp drive) was the "original", basic subspace warp technology that any FTL spacefaring civilization in the TOS Universe would be expected to use. In my TOS-derived "worldview" that I submitted to the roundtable, this classic warp technology used a single set of coils in each of the ship's two warp nacelles to form the warp-field, enabling "third-power" FTL velocities per warp factor.
But the Klingons developed a more elaborate technology, using rectangular nacelles with smaller, more compact coils arranged in two sets per nacelle. What fannon called "linear warp drive" arose from a crude Klingon attempt to get two sets of warp fields to intersect on the axis of motion, producing "fourth power" FTL velocities. The Federation saw the strategic potential and tried in haste to catch up with the Klingons, and ultimately both powers perfected linear warp drive. So when the refit Enterprise finally got over its wormhole problems and get underway at Warp 7, Linear Warp 7 would be seven times faster than the older single-subspace Warp 7 seen in TOS. (This also explains Picard's four-nacelle Stargazer, if we assume that each pod has only one set of coils.)
Transwarp was attempted with Excelsior, trying to use three sets of coils per nacelle to produce a "fifth-power" stardrive, but balancing the three sets of coils proved to be beyond Federation engineering abilities. So Excelsior wound up being just a newer, improved generation of super-heavy cruiser with "fourth power" linear warp drive.
The mathematics of it would be that even though a TOS-era Connie could strain itself to sprint at Warp 8 and risk explosion to go Warp 14.1, a linear-warp-driven refit of the same ship could cruise on by at Linear Warp 5 or sprint at Warp 7.3.
So the technology in the nacelles, borrowed from the Klingons, was the real "arms race" in the TMP era. The key was getting more FTL speed per warp factor, rather than more nacelles for higher warp speeds.