I use a dewey coating clearning rod which I've always thouht were very good. Ball Bearing?
So you don't run a brush at all? Are you able to get all copper fouling out with just jags and patches? Have you not cleaned your rifle for a week or two after shooting and are still able to get all of the carbon out?
I use a Dewey (nylon coated) rod as well- the ball bearing is in the handle which allows the rod to spin without resistance conforming to the twist of the rifling
No brushes for me. But, that's just personal preference, out of an abundance of caution. Here's an article polling top shooters and manufacturers, and there's a reference to Wipe-Out as well at the beginning.
We generally shoot once a month (sometimes more if we can, but it's a two-hour drive each way to the 1000 yard range), and depending on my round count, one of the rifles may get cleaned after, others not. Leaving carbon/powder fouling in the rifle (we're not talking corrosive primers here) has no adverse affects- especially when they're stored in conditioned (cool, dry) spaces. Might go two months between cleanings, might get cleaned when I get home- depends on the rifle, and how it was shooting. If I put fifty rounds down the tube and it was really in the groove when I packed it up, I usually don't mess with it.
OTOH, if accuracy was beginning to drop off- it gets a going through.
"Stubborn" carbon fouling is another issue. I had never seen "carbon ring" before until last year. My son's AR-15 is chambered in 6.5 Grendel for long-range target. He had been "cleaning" it- but had neglected to do visual inspections of the bore after. Accuracy had gone in the crapper, gradually then increasingly worse over two range trips.
I pulled the BCG and looked down the bore. There was this thick black ring, just ahead of the chamber. You could actually feel the restriction running a patch/jag down the bore. I can only contribute it to the powder (8208) as I've never had an issue like that with any other powder (and his loads aren't particularly hot).
It took an entire night of Carb-Out and JB Bore paste to get it cleaned up. Moral of the story- however /whenever you choose to clean, do a visual inspection of the bore if possible after.