Although the OP is satisfied with the answer to their question, @henning-kockerbeck also nails it on the head, but for a different reason.
It's a question of which came first, and in this case, the Enterprise being filmed left to right came last, and film theory as taught in Western culture, came first.
With regards to the Enterprise TOS model, someone had to make the decision before of: which side was going to get the wiring put in. (I know the model was originally built sans internals, but IIRC the detailing was already bias to starboard)
The usual case is that a bunch of story boards are made up in pre-production.
These little 'picture-grams' give an idea of the movement or action on screen and usually gives visual cues as to direction of travel and movement, usually again with arrows and or descriptions.
The model shop with this knowledge and through experience then builds the model, knowing that at least one of the sides is going to be fitted with not only wiring but also the supporting rod for when it gets filmed.
Now this is where it fits for the TOS model only - the model builder built his models a particular way, and not in a way that is commonly used for filming physical models, true even back then and especially true today (ignoring CGI).
This then meant that even if storyboards dictated a different direction, they had to film it with reversed decals and then flip it (as mentioned in other answers).
This is not normal.
This is only for the eleven foot model.
All other sizes of the model could have been filmed from other angles.
In fact the eleven foot model was mostly ignored once the 'beauty' shots were done, as it was the other, smaller, models that got all the 'action' shots instead.
This also led to the rebuilding of the model to make it 'proper' for filming when they went to the big screen and beyond (in addition to the original model not being loaned out).
This meant the physical model, at the very least, is built, complete, all around (using the Enterprise as the example), with around 5 points for the armature rods to be plugged into.
This then allows the model to be filmed from a variety of angles as dictated by the director.
As the OP mentions Star Trek Next Generation too, then the following applies:
So although the OP's preferred answer is technically correct, especially for the singular eleven foot model in ST:TOS, in almost all other cases building the model that way is not the reason it was filmed that way.
The reason for this is because the director, together with the storyboard artist and possibly the writer, would have put it down on paper that way, and it is the culmination of theory that is taught, consciously or otherwise, that people accept seeing things go a certain way to indicate a protagonist or an antagonist, in film.
The old Good vs. Bad.
But where does this come from?
..right and left hands are tied to positive and negative depictions in
Some religions have held (perhaps only in passing discussion) that the
right hand is that of good, and the left hand is that of evil, and as
such it seemed a natural fit into understanding the underlying
semiotics of directionality and affect.
...clearly not the most direct influence but it may have effects on a
more cultural level.
The horizontally drawn cross is left to right.
Read this article:Why a Characters Lateral Movement On-Screen Matters in Film
The footage that showed right to left lateral movement made the
participants feel bad. They responded that watching the footage
made them have more negative feelings than the footage in which the
lateral movement went from left to right. ... our culture has trained
our brains to view left to right movement as an indicator or progress
and it refers to a dead link which is now a pdf:
Directionality of Film Character and Camera Movement
The primacy of the “right” hand is often repeated in popular culture,
and the films themselves reflect this perspective. For example, an
important monologue from the classic film Night of the Hunter (1955)
overtly describes this belief structure:
Would you like me to tell you the little story of right hand left hand?
The story of good and evil?
H-A-T-E…it was with this left hand that old brother Cain struck the blow that laid his brother low.
L-O-V-E…you see these fingers, dear hearts?
These fingers has veins that run straight to the soul of man.
The right hand, friends, the hand of love.
The Cruel Sea, uses ships of a different kind, and shows that the direction a hero takes is not related just to a fight but rather its journey too, as described in Donald Sinden's "Laughter in the Second Act":
The editor, Peter Tanner, showed me a clip of film in which the Compass Rose was sailing from left to right across the screen. 'Now, that is exactly the shot I need to show the ship returning to Liverpool – but the ship is going the wrong way.' I asked him what he meant and he said 'The eye of the viewer accepts anything travelling from left to right as going away from home, anything going from right to left is returning home.
And since film predates videogames, you see this in videogames too:
For example, a number of video games have featured left to right
movement as the dominant direction. The Atari 2600 game Pitfall!
(1982) pioneered the popular side-scrolling platform genre in which
the main character “is seen from the side and typically moves from
left to right as the background and structures continuously appear on
the right and disappear on the left”
...the iconic, mega-selling Super Mario Bros. “Horizontal scroll” was
a common aesthetic feature of games in the 80s,
titles that feature it as ones in which “the player character would
fight his way from left to right, by either battling or avoiding
This seems to point to a universality of the primacy of the “right,”
that is robust and enduring...
(My addition) in Western culture...
Here's another example, illustrating the use of concept artwork and use of directions or visual cues in storyboards:
Of course, (film) rules are made to be broken:
(I know, I know, Star Wars Episode IV's attack on the Death Star is right to left, and just goes to show that it is not a hard and fast rule, but in absence of a directors direction, it is the fall back 'guideline', or perhaps, trope. And usually, if it is established in that direction, visual consistency then usually flows thereafter. Modern tv and film has shown that the audience can accept both directions without questioning it, and also that the audience is now very much beyond just the western world)
So, to summarize: the ones-sided nature of eleven foot model forced filming on that side, but it is not by any means the sole reason for having filmed in that particular direction on screen