Why was the Death Star's tractor beam not used as a weapon during the battles?

A comment on an answer I posted points out that there was at least suspicion that the fighters in the Battle of Yavin were a threat:

Moradmin Bast: "We've analyzed their attack, sir, and there is a danger. Should I have your ship standing by?"

Grand Moff Tarkin: "Evacuate? In our moment of triumph? I think you overestimate their chances!"

This was in response to the part of my answer citing the fighters' vulnerability to tractor beams:

The second issue is the tractor beam. Small craft such as x-wings would likely have been easy targets for the tractor beam. They were ignored when they seemed to be providing general cover fire, and once they were inside the trench they would likely have been untargetable by the tractor beam. However, if it became clear that they were the real point of the attack, and were focused on a weakness within the Death Star, it would have taken very little effort to use the tractor beam to simply smash the Y-wing and X-wing craft against the surface of the Death Star.

I mentioned this because, to my understanding, military-grade tractor beams seem to have been extremely effective against small fighters.

Even Luke Skywalker, 9 years after the battle of Yavin and a full Jedi, had difficulty escaping when Grand Admiral Thrawn's flagship Chimera locked their tractor beam onto his X-Wing.

The first Death Star had 768 tractor beam generators, and was capable of easily capturing even the Millenium Falcon.

Why didn't the Imperials simply start grabbing fighters with the tractor beam and fling them into each other, crash them onto the surface of the Death Star, or even just hold them motionless so the turbo-lasers and TIE-fighters could destroy them?

Answer

For the second battle, it seems clear that the Imperial Fleet's focus was not on smaller fighters, but rather on the Rebel Fleet, which was much more easily handled by the use of Super Star Destroyers and the Death Star's main cannon, which took up considerable power.

For the first battle...it seems pretty obvious why they didn't use the tractor beam. It was disabled when they rescued Princess Leia. You might argue that they would have repaired it in the intermitten time, but considering they were preparing for full battle, and to destroy Yavin IV, resources were likely allocated towards preparing the planet-destroying laser. They may have also not bothered because they figured their turret defenses would be able to stop any assault - but did not factor in the small size of the ships that were attacking, and thus didn't prepare for the possibility of such an assault.

In short, they hadn't yet brought the tractor beams back up from when they saved Princess Leia, and hadn't considered countermeasures to a small-fighter assault, which is ultimately why the attack worked at all.