Most of the time, the Federation hadn't really dabbled in faster than Warp propulsion development in TNG era.
Individual ships encountered it and their crews then dabbled with it to create their own version.
The Coaxial drive was actually fixed at the end of that particular episode, but neatly forgotten.
Quantum Slipstream was effectively the only technology used by the crew on 2 separate occasions.
It's no wonder their second attempt would produce questionable results, but that was more due to the inefficiency of their computers that were too slow at the time to properly calculate the phase variance as it was forming.
However, if the Federation was to create the Quantum drive and pick up from where Voyager left off... well, one can easily claim that several years after the ship made it back to Federation territory, they'd have a functioning QS drive (but still limited by the Benemyte crystals).
Or they can use the slower version of the drive that would have initially took them about 3 months to traverse 60 000 ly's (that one Voyager hadn't had a problem with when it came to the phase variance, but rather with the hull being unable to take quantum stresses).
QS as such is viable for Feds to acomplish.
Transwarp ... seeing how it's similar to QS in the first place, development of the latter should provide insight into reaching it (though, on their v2 of QS, we were led to think it was on par, if not better than TW).
Higher Warp velocities are more or less a given.
SF is bound to increase the efficiency of regular Warp engines as well, which would probably bring everything to early TNG standards and reduce travel significantly.