In any case, it's the kind of issue that will come with trying to make space war = World War II so closely. I count myself among those that enjoy this movie, regardless of such issues.
Interestingly, in some of the earlier versions of this scene, rather than a tractor, the Claw has some kind of automatic shunting system where big metal paddles sweep the deck automatically. There's no tractor that needs to go out the airlock, and thus avoids the "it would have taken the same amount of time to push her in" problem. It doesn't answer why the other fighters can't just maneuver around the rapier... though perhaps the artificial gravity means that the fighters have to maintain a certain amount of momentum on the way into the hangar. It also explains why Maniac doesn't seem to know what a tractor is when he's yelling "what is that!" and then pleading with the flight boss to stop the process.
The scene as a whole is probably the most problematic one in the movie, moreso than any Pilgrim stuff or the "never existed" subplot. We see rapiers maneuver directly vertically earlier in the movie even with the Jack-in-the-box move. The bay the Diligent parks in is a separate bay though with a separate door and presumably, at the point Rosie crashes, the Diligent is still parked there, so the bay isn't available for Rapiers.You'd still ask why the paddles don't sweep inwards towards the enclosed airspace area. Also, we see the Diligent land vertically into a landing bay when it first arrives at the Claw, so there's certainly ways for craft to maneuver into landing position.