Breaking in a barrell is a myth started by gunsmiths that make barrells commercially. The more rounds they can get you to shoot through their barrell breaking it in, means it wears out quicker and you get to buy another barrell from them, especially in the larger calibers. It's all bs.

If barrels wear out by chooting them then breaking them in is not a myth.
Its not rocket science, 100 rounds down the pipe smoothes things out

I have a new .308 T/C Encore and it has yet to produse tight groups at 100 yds. I strictly followed a "break-in" proceedure of cleaning after every shot, then after every 5 shots, then 10 and so on.
I checked with a couple bench shooters I know who love the .308 and they said it could take 50 or more rounds in their experience to get tight groups.
So be patient, clean it a lot, and keep shooting. You can't shoot too much.

As far as wearing out a barrel . . . maybe in the magnum calibers . . . that's one of the reasons bench shooters don't use them. That and shoulder fatigue.