I don't think it's that strange to have the latest design of a ship feature a prototype technology that's apparently somewhat controversial (Scotty, at minimum, seems to have a huge problem with it) when it clearly has it's advantages and supporters. The technology must have at least worked out on paper, and proven itself in some testing, but for a full-scale test it might need some accommodations that only a brand new ship design could deliver.
And it's not clear what the "transwarp" in the Excelsior was exactly. All "transwarp" means, technically speaking, is "beyond warp". And when they said "all speeds available through transwarp", I kind of took that to mean an acceleration factor, not infinity speed like in that Voyager episode with the lizards, or the Borg's space-tunnels. If the Enterprise took off at warp, it might take a few moments to reach warp nine, and then have difficulty maintaining that maximum speed. The Excelsior might hit warp nine effortlessly, in an instant, and then maintain that speed indefinitely. That would be considered "beyond" what TOS-era warp drives were thought to be capable of, and would allow Excelsior to break Enterprise's speed records, and would provide a rude awakening for anyone trying to run off with the Enterprise.
And apparently Scotty's sabotage of the Excelsior provided a huge setback for the technology. It's apparently overcomplicated, easily broken, and completely non-fuctional when things aren't going exactly as planned (although that could have something to do with the fact that it was a prototype). That's the sort of technology that looks good on paper and you could see a good number of people being convinced by it, but it wouldn't fly with a veteran like Scotty who knows how durable and resilient an engine needs to be when it gets treated roughly out there in the real world.
The Excelsior was apparently retrofitted, and a standard warp drive was installed for Captain Sulu. Just the fact that this is possible means that both engine types were taken into consideration when designing the Excelsior, and the failure of this new technology wasn't something that blindsided them. But that didn't stop them from making some room for it in the newest ship design, and giving it every chance to succeed.
But for all we know, the definition of "transwarp" might have changed over the years, and Picard's Enterprise might incorporate a refined version of Excelsior's technology. Remember, Scotty eventually said that he didn't particularly like Picard's Enterprise. He said that in his day he could tell you what speed you were going from the feel of the vibrations in the deck plates, but Picard's Enterprise doesn't do that anymore. Scotty would have to go back to school to re-learn how Picard's engines even work.