It's entirely possible that Excelsior was not built around the special drive so much as she was, in development, so much better suited for its testing than any other ship that she was diverted from the regular workflow and reengineered for the test.
I doubt they would have diverted the pathfinder of the class into a side project that would not have required nearly the capital expenditure to prove. It seems far more likely that long before TWOK and perhaps before TMP, transwarp was shown to work and incorporated into the Excelsior specs.
What does Scotty say about it? He says, "If my grandmother had wheels, she'd be a wagon." This is not a highly technical dissection of the Excelsior's inner workings. In fact, it seems more in line with the same conservatism on display (if compounded by loneliness) in Relics.
Iirc, from that episode, initially LaForge is (if dickishly) almost contemptuous of Scotty's expertise, lending credence to the notion that something fundamental has changed about warp theory and practice. By way of analogy, if Karl Benz came back from the dead, he might well be capable of fixing your car, because, rampant computerization aside, internal combustion engines do still operate on the same principles. If James Thomson came back, however, and wanted to fiddle with my computer's innards, I wouldn't let him, because although he invented a analog differential equation solving computer, he might try to do something hydraulic to my motherboard and its digital operating principles.
But let's digress from Scotty and his sour grapes--and listen to what
Sulu says. This here is a master flight controller. Surely he's up on the next big thing in spaceflight, and he seems impressed but not incredulous. The capabilities of a drive system and the speed of a ship are no doubt of as paramountly important to him as they are to an engineer. Sulu would know at least as well as Scotty. Kirk, for what it's worth, also appears receptive to the transwarp "great experiment."
In the next film, Sulu remarks that he's
hoping for a post on the Excelsior. By TUC, Sulu's gotten his dream job and his dream ship. I wonder: would he have been so bent on attaining the captaincy of the Excelsior if she had been, as you assert, a failure?
It would seem silly to argue that the drive was a success when it seems very clear that she spent years in spacedock after the failed test, emerged with a different configuration, and no one ever mentioned a homegrown transwarp per se again.
Excelsior herself is mentioned once, in TVH, in a positive manner, and seen briefly in TUC. But if transwarp had not been mentioned at all, in six hours of screentime in films focusing on a different ship and one of which took place 90% in 1985, I wouldn't suppose that's conclusive evidence of her failure. I sometimes go whole days without mentioning transwarp drive.

By TNG, of course, transwarp = warp.
It is really stretching it that such a buzz was made over transwarp and its different systems and engineering, only for us to accept that after a successful test, it was rapidly engineered into mostly every other Federation ship we ever saw without further comment. Moreover, this makes the whole issue of its needing to be tested on Excelsior into a strange one, because there would be a strong implication of its easy retrofit into designs that we know are older, such as the Miranda class.
Miranda is indeed the oldest ship we know of that might have been refitted with tranwarp. It is somewhat implicit that Mirandas can keep up during fleet actions with Excelsiors and Galaxies. I would remark that the Miranda is (far) newer than the Constitution, the application of transwarp to whose spaceframe failed, if it were attempted at all.
Again, this is not impossible, but all seems like a lot of work to justify something that wouldn't mean much in the long run, let alone the fact that "transwarp" in the TNG era seems to have the same general meaning as a beyond-warp-drive kind of thing...are we really to figure that all the buzz about the new drive would fade as every other ship got it and the term would come back into use to mean "trans-transwarp?" I know this is not impossible because of the way people create conversational shorthand, but we need to remember that this is what passed for technobabble, and was probably supposed to have a more technical (if potentially classified in-universe) meaning as it was used in the movie.
Stranger things have happened. If we routinely traveled at multiples of the speed of sound as the denizens of Trek travel at multiples of the speed of light, I suspect "hypersonic" would lose a lot of its buzz over a period of a century. "Hypersonic" today might be Mach 5+, but if hundreds of different spaceplanes are already going Mach 50 and there's a new one that can go Mach 500, "hypersonic" would attach more readily, imo, to the Mach 500. "Mach 500: the new hypersonic" would appear on the cover of Popular Mechanics and such other publications.
Speaking as a writer, I can't get past the pointlessness of introducing a new drive with such heavy skepticism from the engineer character among Our Heroes if it was supposed to "really" be a success.
And such cheerful enthusiasm from our accomplished pilot and acceptance by our godlike captain...
The movie introduces it this way, nothing else ever references it directly, the ships in TNG are not so much faster than those of TOS by the backstage values for each production (and are in fact notably slower than certain speeds thrown around for TOS warp...doesn't the Enterprise travel 990.7 LY in a couple of days at most in "That Which Survives")...
So TOS didn't do astronomical distances well. No Trek never has. They say she has transplot speed?
I don't feel that there are hidden clues telling us to believe it was a success in the direct sense, nor that we'd gain much by devaluing the term "transwarp" to the point where it could have been.
I don't think it does devalue it. Rather the opposite: it revalues it by evolving the word. If the Federation was on the brink of discovering the propulsion capabilities of the Borg in the 23rd century, I think
that would devalue transwarp. If they
gave up, I think that devalues Starfleet.
Maybe Starfleet got way too excited about potential implications of a new breakthrough and tried to put it into practice, only to experience a costly failure in the realization that it either wasn't ready for prime time or couldn't be made that way for some more fundamental reason; I think there are a lot of real-world stories that mirror this.
The production history of the Excelsior begs to differ. The ships served as the backbone of Starfleet for a century. They would have served as that for even longer, except by the 2370s, they simply weren't first-rate warships anymore, and the Dominion blew a lot of them up. It seems unlikely that a navy would build dozens or potentially hundreds or thousands of ships when the first sucked. There is even some suggestion from the reg numbers that a new run of Excelsiors was commissioned in the mid-23rd century--but I realize this is weakly persuasive at best!
However, add to that the change in warp scales that happened sometime after TUC, and you have a preponderance of evidence that transwarp worked, and still worked, in 2379, the last canonical appearance of a Starfleet vessel with engines of the Excelsior type.