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ships, like the Jenolan, will still run rings around ships like the Enterprise, even though it is nearly a full century out of date.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.
Starships are fast but they really shouldn't be that maneuverable. You do still have to worry about the inertial dampeners. If you're constantly changing directions, the inertial dampeners have to compensate for the acceleration. Keep in mind that starships can accelerate at rates that would flatten anyone into bloody goo without inertial dampeners.
Even if they're always using a warp bubble to change the ship's mass, it would not be easy to compensate for quickly accelerating to 0.1c, going down to 0, and then immediately accelerating to 0.1c to another direction.
On the other hand, the ship not being able to accelerate that quickly due to the limitations of its inertial dampening system, should also be factored in. There's not much point to saying that a Galaxy class starship can accelerate to Warp 9 from a standstill in a third of a millisecond, if the actual time it needs is about 10 seconds, because it would otherwise overwhelm its inertial dampeners.
We are given an example of a ship basically going -0.1c to Warp 9, since the specific example is "from slow reverse impulse to Warp 9 in 0.3 milliseconds". Logically, it should also be able to accelerate to only a portion of that speed, or use the engines to stop just as quickly.
But warp speed isn't the same as impulse. Warp doesn't accelerate based on Newtonian principles. It's bending space in a bubble around the ship. That's how it's able to go faster than the speed of light.
Changing directions at warp has other issues. From what we've seen, they actually have to drop out of warp in order to make large course corrections.