I've used most of the cut-rifled makers, and several button mfgs.
Bartlein doesn't outright forbid them. They do say they suggest going a size smaller than the bore. In a blog post, Frank says he doesn't use them, but acknowledges folks do, and urges caution as debris can get trapped in the bristles.
Their cleaning regimen seems to conflict with a lot of what's been posted in this thread too (folks are talking bore snakes lol).
https://bartleinbarrels.com/break-in-and-cleaning/
Jackson, WI
bartleinbarrels.com
In my own experience (with a borescope) it's been my observation that no chemical can outright remove hard-carbon (I'm not talking about powder residue), and it only becomes harder to remove as time goes on. I don't necessarily think it needs to be cleaned down to bare metal, but I do think it's easier to 'stay on top of' carbon buildup so it doesn't become an impossible job later down the line.
I think the reason brushes get folks worried is because if you use the wrong material, or the wrong techniques, you absolutely can hurt a barrel with one. That said, if you're using a 1-piece coated rod, tight bore guide, bronze/nylon brush, keeping it clean & saturated, and not going across the crown aggressively...I think you're relatively safe. As long as you follow these same techniques, and don't over-use JB (along with realizing it ALWAYS comes out black) I think you can be safe with it is as well. You can feel patches go down the barrel easier as you brush and/or JB vs. just patching alone.
I will say there's an outstanding article over on accurateshooter which covers multiple shooters (and disciplines) and barrel makers; the interesting thing is that their routines and recommendations are all over the board with regards to brushing. Almost none of them however advocate shooting for hundreds of rounds (not that you are advocating such a thing in your above post).
Link to article:
https://www.accurateshooter.com/technical-articles/barrel-cleaning-debate/
I'm an F-Class guy, so I clean like most of the others there. This board is mostly PRS shooters, so maybe brushing and carbon maintenance isn't as big a deal there; never shot a PRS match, so I don't know.