I admit I am an ignorant in regards to the Wing Commander series, so I cannot really participate in the discussion in a meaningful way.
The only entry of that saga that I have played was Privateer, but I played it for many many years.

Perhaps I was too used to the X-wing flight model, but I never felt the need of using any sliding maneuvers while dogfighting in Privateer. Perhaps it was most effective against bigger ships?

I play a lot of Elite Dangerous, and that game has a mix of newtonian and non-newtonian physics with the flight assist thingie. You can spin around while keeping your velocity to aim your weapons to where you want.

I will say, and please feel free to correct me, these spins and slides would not be really effective in the X-wing series, even if we added them. And I think so for these reasons:

- As you have mentioned, AI in the X-wing series is terrified of flying on a straight line. Sliding, as in your ship keeping its current velocity vector while its nose actually aims elsewhere, wouldn't be really different from firing a turret from a ship that moves on a straight line, right?
Well, since the AI would be turning left and right to get away from your firing arc and getting an arc of its own, it wouldn't really be much easier to hit. You would need to lead a target that is moving erratically on a direction that is perpendicular to where you are looking at. This is usually much harder than firing at a ship from behind or from the front, because the leading distance covers a bigger angle of your view.

- Flying on a straight line in the X-wing series during a dogfight means imminent death for you (that is why getting the flight control system damaged means death most of the time). The AI leads its targets pretty well if they fly on a straight like, so even while you would be spinning around to get a shot on your target, you would be an even much easier target yourself since you would keep flying in the same bearing you had before "disabling the non-newtonian mode".
Remember that dogfights in Star Wars rarely involve only 2 ships. Most of the time it's a rebel ship ganked by 3 or more fighters. Even in the case that your sliding or spinning allows you to down one pursuer, you'd have two more firing at a target moving on a straight line.

- While the Privateer manual recommended using the sliding technique against bigger ships, I think it would be a terrible terrible idea in X-wing. Capital ships are dotted with turrets that lead their targets very well even at distances of kilometers. They are usually easy to deal with if you use flying wavy patterns or spiral patterns to approach, disengage or navigate close to them.
Definitely, sliding to attack a frigate or corvette would mean that you are blown up pretty fast since you are a as much a sitting duck by moving on a straight line as if you were actually sitting on the spot. You cannot fool the AI with speed. Only with constant changes of direction.

- The X-wing series got to have their own version of this spinning around from XvT and on, in the sense that by lowering your throttle dramatically increased your angular acceleration, allowing your ship to turn much faster than it usually could in X-Wing and TIE Fighter.
My personal opinion doesn't matter, but I never liked this, since it turned the clumsiest B-wing into a TIE Interceptor just by taking your foot off the gas pedal. That didn't make any sense to me, and I actually believe that was detrimental for the series, because it evened out all fighters by making them all as agile in dogfights as any other. Slumbering Y-wings would turn now on a dime to shoot down the fighter that flew past it.
I remember modding the Assault Transport so that it would be flyable in multiplayer skirmishes, and that was ridiculous, when you could lower the throttle to 33% for a second and let you spin around like a madman in such big ship 6-8 frontal cannons...

- There is actually one maneuver in the X-wing series that the AI can do but the player can't. It reminds to sliding but in a very different way. I call it "drifting" or "strafing" in the code because it isn't properly referenced anywhere else in the manuals. It's an undocumented feature that is used by the AI bombers while attacking capital ships to survive the ship's turrets.
It consists on moving laterally or up and down without actually changing their bearing or velocity vector. This movement is very subtle, practically imperceptible if you don't know what you are looking at. As if done not by the engines, but by the repursorlift projectors of the ship. It's never faster than 3-5 meters per second or around that, so it's not like you can use it to evade starfighter fire.
However it is effective when facing a capital ship. The AI strafes erratically in this way, up, down, left, right... randomly. That is enough to confuse the target leading of turrets and get hit less often than if it flew in an actual straight line.
For some time I considered letting the player do this with the help of holding some button or something like that. But I think it could break balance a bit.