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ships, like the Jenolan, will still run rings around ships like the Enterprise, even though it is nearly a full century out of date.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.
Just in the spirit of shows underselling ship capabilities, I could see a federation flagship having a potentially better agility to mass ratio than a basic shuttle any civilian could pilot for leisure.