What would one consider sufficient clearance on a neck?
In theory, 0.001" is enough. In practice, you need more for case variance and carbon build up. 0.004" is common for LR chambers that are going to be running high pressure loads and firing lots of rounds. Benchresters can get away with less because they clean frequently. If you're running a no-turn neck, and you want to be able to fire factory ammo, use brass right out of the box or are using SS media, you should have more.
Let look at that in more detail. New cases and cases that have been tumbled in SS media have case mouths that are peened (mushroomed). You can see it looking at them.
The mouth has been beaten down. If you looked at a sectioned view of the case mouth, it would look similar to this (same effect):
If you run your finger nail along the edge of the case neck over the case mouth, you can feel the overhang of the mushroomed material. If you can feel the overhand, there is at least 0.001" of material on either side of the case mouth (inside and outside). Once you seat a bullet, the inside gets pushed to the outside, and you now have a 0.002" ring around the case mouth of material above and beyond the thickness of your neck. If your chamber was designed with 0.004" clearance over the neck wall thickness, you now have contact between the chamber wall and the mushroomed material. That mushroomed material is being pinched between the bullet and the chamber wall. Since the mushroomed material is not consistent, the tension this creates on the bullet will not be consistent and the loads will never shoot as well as they would if you had a clean bullet release.
Neck turning removes all traces of the mushroomed material from new cases. If you tumble with SS media, the mushroom will return. How much depends on how long you tumble for, but it will return to some degree. If it is not fully removed, it may create interference again as described above. Mic a loaded case neck below the case mouth and right on the case mouth and you will be able to tell very quickly if there is still anything left of the burr (mushroomed overhang).