I have had no problems with accuracy from pulled bullets using the inertia puller, the collet puller works great but the bullets are ruined 100% of the time.
This, I can not understand. I have the Hornady collet puller and have used it for nearly ten years to pull many hundreds of bullets. It has never left a mark on a cup and core, or on a mono-metal in 6mm, 6.5 mm, or 7mm.
I do not have collets for 22 or 30 cal. But there are 3 inertia pullers in the drawer for those.
I use the Hornady Collet Puller in a Coax. As long as there's bullet bearing surface to grab, the only time I've messed up a bullet it's been my fault, e.g. I used the wrong collet (usually knowingly), had collet too tight, manhandled lever, etc.. Run the collet down to within a half hair off the case mouth and grab the bullet by the bearing surface with just enough grip to extract it plus a smidgen.
Assuming you've got bearing surface to grab, if your wrecking bullets, then either you have the puller adjusted with too much grip or it's a neck tension/crimp issue. I run minimal neck tension. The smaller the bullet the trickier. I did wreck a few .204 bullets back when I first started using the Hornady Collet Puller.
My thinking has been, any slight surface damage to the bearing surface will get worked out by a trip down the bore. Regardless, If there's any doubt a bullet was damaged, it gets used in a fouler or velocity check. This choice is a function of an unsubstantiated belief that pulled bullets are substandard.* It should be noted that, the bulk of my loading these days is for matches ranging to 1200 yrds. or practice for said matches.
I don't typically pull too many bullets. If I did, I wouldn't be loading them in match rounds, regardless of how they were pulled. *See above.