Follow the manufacturer's recommendation. Some barrels won't need breaking in, some will show benefit. Done properly it doesn't hurt anything, and the potential benefit is in reducing fouling later.
I have yet to see hard data on the effect on accuracy, but the average shooter is not generally good enough to be able to tell the difference regardless.
IMO, that's going overboard. It's funny how the people who recommend this procedure are ALWAYS selling one or more of the components required to do it. I do agree with cleaning the bore before firing for the first time...
1. Patch cleaned the bore using Shooter's Choice until all patches were white. I pushed each patch straight through from the bore, not back and forth.
2. Using a brass jag and JB Bore Cleaner (blue label) and Kroil and a bore guide, I ran patches through, back and forth, until it started getting black, then added more compound and Kroil until the patch started feeling loose.
3. Clean the bore again as in step 1.
4. Use JB Bore Polish (red label) in the same manner as step 2.
5. Clean bore again like steps 1 and 3.
After lapping the bore this way I did notice that the bore seemed much brighter than it was after the initial cleaning.
I have never "broken in a barrel", and I have never had an issue. I took my Savage Edge to the range, unfired, and shot 1 group smaller then a dime, and one smaller then a nickle. All I do initialy, is swab the barrel well with a bore snake.
Find out who made the barrel and find out their recommendations. I purchased a custom AR upper that the manufacturer had specific instructions for best results. It requires a little more time than just" shoot it" but I consider it time well spent. Besides, I only ended up cleaning the bore 13 times in one day. It probably cost me 50 cents and time.
^This^
I bought my Savage 10FP a month before I went to south Dakota. Sighted it in, did some load development, went to S.D. and shot 1000 rounds through it. No break in, shoots as good today as it did out of the box.
The M1A I just won, cleaned it went out and shot about 100 rounds through it and didn't clean it till I got home.