I’m rewatching TOS on Blu-ray and aside from the usual examples of higher speeds than expected (like the trip of a thousand light-years in “Obsession”), it’s particularly noticeable when characters casually refer to “the galaxy” in situations where a century later they’d be speaking of “the quadrant” or “the Alpha Quadrant”. Not more than the galaxy, but not less either.
It’s just a subtle difference in scale that seems to have been lost during the production of TNG, and I’d also argue that we need to question the usual assumption where the same warp factor represents a higher speed on TNG: what if it’s actually lower but safer on average, as opposed to the constant nervousness about reaching Warp 7 or higher on TOS? Maybe Kirk visited a lot of the areas that would later be classified as the Delta Quadrant or the Gamma Quadrant — it just wasn’t followed up on necessarily.
The writers were bad with consistency.
I actually like the excessively high warp speeds that allow a ship to travel through a 1000 ly's in a short amount of time like in TOS (say a day)... as it illustrates what a combination of multiple alien species working together could achieve in 100 years since the Federation was founded.
Quite frankly, TNG should have been as Roddenberry originally intended (for Enterprise-D to be exploring other galaxies)
But then TNG writers scaled down and resulted in Warp speeds being excessively slow.
Warp 9.9 was actually confirmed to be about 21 473 x Light speed on Voyager by Tom Paris (speed which the ship never managed to achieve... actually no TNG ships were able to achieve that speed with stock engine setup when they launched)... and Voyager was usually cruising at Warp 6 back to the Alpha Quadrant.
The USS Prometheus (as seen on Voyager), was the first SF ship able to achieve Warp 9.9 and hold it without shaking apart - so at least we have some canonical data which says that in the late 24th century (or at least 4 years after Voyager launched), SF managed to create ships capable of achieving Warp 9.9 as a cruising velocity.
To me, it seemed like TOS and the movies which portray similarly high Warp speeds actually occurred in an alternate universe.
Whereas TNG, DS9 and VOY are in their own universe, and had a version of TOS happening, just slower Warp speeds compared to what we saw in the 24th century.
I don't mind consistency, but Trek writers were BAD at predicting/imagining how far the Federation would realistically evolve, which actually resulted in very little to nothing really changing between the end of Voyager and by the time we saw Star Trek Picard for example (which takes place 20 years later).
Even Discovery managed to mess it up, with journeys still taking months at Warp in the 32nd century (which is extremely unrealistic).
By the 24th century, SF was able to effectively 'double' Warp velocity. And the late 24th century also brought about various innovations and pretty big increases in Warp drive speeds (because every increment past Warp 9.9 results in doubling of speed).
But, even if we assume that the Federation was only able to double Warp speeds every century after Voyager returned to the Alpha Quadrant... by the 31st century (aka just prior to the Burn) it would be something like this:
Warp 9.9 (mid/late 24th century) = 21,473 times LS
Warp 9.91 (mid 25th century) = 42,946 times LS
Warp 9.92 (mid 26th century) = 85,892 times LS
Warp 9.93 (mid 27th century) = 171,784 times LS
Warp 9.94 (mid 28th century) = 343,568 times LS
Warp 9.95 (mid 29th century) = 687,136 times LS
Warp 9.96 (mid 30th century) = 1,374,272 times LS
Warp 9.97 (mid 31st century - just prior to the Burn) = 2,748,544 times LS.
But, doubling speed every century is a highly conservative estimate which doesn't take into account exponential developments and returns in science and technology which would effectively result in something akin to 1000x - 1 million times improvements from the 24th to the 25th century - and 25th to 26th would be akin to billion or trillion times improvements - this would be accurate for just 1 species... and on TOP of that you'd have to add in influx of added technological/scientific and diverse knowledge bases (not to mention capabilities) of dozens to 150 other alien species - this is why the Federation should have been FAR more advanced and extragalactic (or exploring other galaxies - including Andromeda) by the 24th century.
But bringing it back to doubling of speed of every century:
Even with Warp 9.9, it would take just a notch under 7 years for a ship to go from one end of the Milky Way to the other.
In the 25th century, it would take 3.5 years to do the same... an seeing how the Federation would likely grow more in all that time, ships wouldn't be launching from Utopia Planitia all the time (in fact, U.P. would be just 1 of many shipyards in the entire Federation)... but from other regions of UFP (which are closer to say Gamma and Delta Quadrants).
This also doesn't take into account Quantum Slipstream version 2 which allowed speeds of 10 000 Ly's per MINUTE... and the first version of Quantum Slipstream allowed for speeds of 300 Ly's per hour (or just a notch under Warp 9.97).
Version 1 of QS did produce quantum stressed on Voy hull, but that doesn't mean SF wouldn't be able to study this technology in detail and create reinforced structural integrity fields, etc. which would negate those effects.
And, V1 of QS didn't need Benamite Crystals... only Version 2 did... and I reckon that if Voy was able to make V2 of QS in just 4 months after encountering v1 of the technology, I'd imagine SF with all of its resources would be able to solve the phase variance issue in about 4 months, and probably find a way to synthesize Benamite Crystals in days or hours... as opposed to years, and either slow their decay drastically, or find means to recrystalize them (perhaps an analogue of Dilithium crystal recrystallization technology).
I mean, we're talking about 150 different space faring (and technologically advanced) alien species working together.
I seriously think the writers heavily understated how fast the Federation would progress.