It's also rather difficult to ignore the conceit that after warp technicians have been trying to reach warp 10 all over the galaxy for centuries, Paris figures it out on his own in a few weeks.
That would be like if I woke up tomorrow and suddenly cured cancer.
And ALSO rather difficult to ignore the fact that going warp 9.99999 doesn't turn you into lizards but does get you home in a few seconds.
People tend to forget that they discovered a new type of dilithium in this episode. That's what allowed them to reach warp 10.
IIRC, it wasn't a new form of dilithium, but actually a different substance that the federation thought was only theoretical; kind of like Omega, but not!
Point taken though!
this is what they said:
PARIS: We discovered a new form of dilithium in the asteroid field we surveyed last month. It remains stable at a much higher warp frequency.