It is all pretty much covered in this section of the linked article. I have bolded the key points!
From a few scrap 9mm pieces of brass to all this (108 posts) good grief!
"Shooters who reload their brass several times may decide to uniform PPs and deburr FHs, especially on their “300-yard and beyond” brass. Here, they will use the cases many times, while the uniforming is performed only once. Also, most handloaders only process moderate amounts of brass, compared to our multi-thousand round lots.
Having high quality Long Range (LR) brass helps. Many of the better brass manufacturers [make] their flash holes so that no burrs are created. Still, it does pay to inspect even THESE manufacturer’s products, as occasional slips are inevitable. Very rarely, some of the best makers will have a significant burr in, say, 1 per 1000 or 2000 cases, and it’s worth catching those.
Exceptions can always be found. Recently, we began processing a large lot of match brass from a premier manufacturer. We were startled to find that every case had a significant burr in the FH — something we’d never before seen from this maker. We then broke out the FH deburring tools and went to work.
Some observers have noted that it can be difficult to truly verify the contribution to accuracy of these procedures — particularly when firing from the shoulder, in conditions. Members of this staff, as individual rifle competitors, do often perform these operations on their privately-owned LR rifle brass. One could ascribe this to the old High Power Rifle maxim that “if you think it helps, then it helps.”
However, a World Champion and Olympic Gold/Silver medalist here commented on his own handloading (for International competition, which demands VERY fine accuracy). He noted that he did seem to see a decline in accuracy whenever he did not uniform FHs, deburr FHs and clean primer pockets before each reloading. (One might be tempted to counter that only a truly World Class shooter could reliably detect the difference.) However, with the wisdom of decades experience, our Champion also remarked that “It could have been that I just wasn’t shooting as well that day.”