I saw this rant/complaint over on Reddit, and it got me thinking a bit.
We know that at least on paper, Federation starships are insanely fast and agile. Data has stated that the Galaxy-class Enterprise was able to achieve Warp 9 from , and some ships, like the Nebula class, don't seem to use impulse engines at all, favouring the warp engine for sublight speed usage at all.
Despite that, we also know that impulse engines aren't simple thrusters, and are able to move the ship in a way not directly in line with the output thrust (Relics), and from the same episode, we also know that smaller ships, like the Jenolan, will still run rings around ships like the Enterprise, even though it is nearly a full century out of date.
However, from what the show itself portrays, the ships tend to be fairly slow and sluggish when in combat, sedately drifting along the battlefield, while weapons fire goes every which way. The most recent and active thing we've seen a big starship do is maybe the fighter run in Picard.
In my opinion, by trying to keep to the slow and seemingly logical expectations for starships to be slow, hulking metal structures that slowly fly around shooting each other, Star Trek ends up underselling what Federation starships are able to do. They would be more realistically portrayed flitting about the battlefield like dragonflies, instead of being like "real boats" today, that have more of a sense of mass.
It seems wildly unintuitive, but it would also help show Federation propulsion technology being more advanced than what they are now. Starships can instantly stop and reverse course, or move in ways that would be impossible with modern technology, and the show not showing ships capable of doing just that might be to its detriment.
If we want to give a daystrom answer I'd argue the reasoning for the inconsistent maneuverability is that targeting computers make it irrelevant in combat. You dont hear about a lot of misses in star trek and they're able to still hit their targets even when at warp speed. So the only time we really see these ships get cooking is if theyre skipping across an atmosphere, running away, or avoiding debris and asteroids.
I suspect there may also be some kind of tactical doctrine where federation ships are meant to hold their ground , give out some warnings, and take a few punches to the nose before going all out. Since they arent going to dodge a phaser anyway they might as well stand firm as a show of strength. Federation policy is very firm about starting a firefight so it's likely need to have the record be very clear that they arent aggressors.
From a meta point of view it's a practical matter of the models for the starships being genuinely big. It is not easy, especially on a 1980s tv budget to make that thing dance around so we got two ships staring each other down via view screen, some dialog about how far away they were, and then reactions of the crew being thrown around as they took hits. Again from a realistic and in universe perspective I think this works. Phasers are super precise, and thanks to shields these ships are tanks. They can dance around but when your that far away that barrel roll isnt going to make much of a difference. But it was clearly technical limitation. We got staredowns and that one shot of the enterprise slowly turning around and warping away.
Once CGI became more common in the mid to late 90s I think the opposite trend wound up happening. DS9 has clouds of federation ships that in theory should be sniping at each other from thousands of KM away charging into a dominion cloud. I think voyager wound up usually striking a better balance of old school staredowns with the occasional cool thing like coming out of warp right on top of someone and blasting them and tractoring another ship away. Enterprise also has quite a lot of maneuvering though the nx class is smaller than the other hero ships.
That does make sense, considering that Federation shields are pretty tough, and the Federation itself probably doesn't want to seem the aggressor by firing first.
For the most part, a Federation ship can just tank a shot with barely a scratch (unless it's an equivalent power), and that might arguably be a better show of force than firing back.
True, I think that many of the complaints are just the differences between the two, although at the same time, with CGI being as cheap as it is, it might also be nice to see them make use of that agility, rather than just having it just be something that only exists in theory.