Have you all forgotten that they directly addressed this in the show? https://youtu.be/Q9W7pvOLxmQ
Risa
Star Trek memes and shitposts
Come on'n get your jamaharon on! There are no real rules—just don't break the weather control network.
I think in this context no ship would ever approach nose-to-nose. That's just for the viewers to see. I'd wager no two ships would come into less than around 1-5 km of each other if they weren't lining up flight paths for shuttles or docking. It's not like they need to "stand up" next to each other and "talk".
They would probably have formations they would assume while in transit or stopped, so it would probably be normal to cross paths with a formation flying upside down or in a perpendicular axis.
In case of just meeting and talking, they'd probably do it from wherever they happen to be, very far from each other, flying towards different destinations. In case of combat, they would behave like a swarm of insects and reorient their formations continuously.
For a ship that never needs aerodynamic control, any shape at all will do so why do they all look like airplanes?
The Borg are the only ones who seem to get this.
Not a trekkie, do they ever land in atmosphere on these ships? You would want aerodynamics for that to reduce drag and thus heat, but I'm not familiar enough to know.
I guess they probably have good thermal protections with their future tech, though.
Voyager does a few times. The Enterprise D did...once.
There are some alternate timeline shenanigans I will not speak of here.
This is why the Borg uses cubes and spheres.
Actually, space in general is mostly 2 dimensional, in that all the interesting stuff generally takes place on some sort of almost flat plane. A star system is generally on a plane, so is the galactic system, and for most planet+moons too. They just tend to be different planes so for ease of communication you will probably just align your idea of down with whatever the most convenient plane is. This of course is ignoring what gravity down is, as that changes as thrust does.
And as for ship alignment, yeah no one is going to worry about that till its time to dock, at which point the lighter vessel will likely change their orientation since its easier and takes less energy. Spaceships are not going to be within human sight range of each other most of the time, even being in relatively the same are. Space too big and getting ships close to each other is dangerous!
But in media that fucks with people's idea of meeting and seeing each other so for convenience of not confusing the audience you don't see that level of realism often.
The galactic plane is 1000 light years deep.
This is why I appreciate the scene in Undiscovered Country where Kronos One glides into view, seeming to align itself to the Enterprise's orientation.