I broke in the last barrel, and it shoots fantastic, but it was a high dollar barrel and it should shoot fantastic. I cannot tell you that a break in process helped or not. I just don't know.
As to the fouling, I was shooting that particular new rifle, which shoots remarkably well, and the groups were just not up to par. I guess I had 75 rounds through it since last cleaning. So I cleaned it (Boretech Eliminator) and it shot great again. That was a 260. My 220 fouls up after about 20 rounds. My 223 will go an easy 50 before it needs cleaning, but I can tell when it's time to clean. Most of the cleaning is carbon fouling. I don't get much copper out of any of the rifles any more.
But, if you want the copper out and you are using some of the ammonia based cleaners, get the Boretech and you'll find copper you didn't know you had. However...I have come to the belief that I don't want absolutely all of the copper out of the bore to get to best accuracy. Once I took all the copper out of my rifles about a year ago, I had to shoot a couple of them enough to lay down a bit more copper to get best accuracy back. A couple of them shot great without copper laydown.
So what I've said above is what I presently think. As with life in general, it's all a work in progress. I may well modify my thinking again, with time.