I don't break in custom barrels at all. A hand lapped barrel will not be "polished" by my cleaning rod. Most bench rest folks and custom barrel makers will tell you that break-in procedures just eat up your shot count of barrel life, so it's not worth the time. (say you break in for 100rnds, on a 2000rnd accuracy life, you wasted 5% of your barrel life, plus your ammo cost. Do that over 10 barrels and you've wasted $250 (half an installed, chambered, and crowned barrel cost).

For factory barrels, I've been in and out of break in procedures. I can say with certainty that I don't believe it has any benefit to accuracy, but I have believed at one point that it did help with cleaning. A few years ago, all of my barrels got a break in. A few barrels later trying without breaking in and I'm not seeing any difference in cleaning.

But sometimes the voodoo that you think works is the voodoo that does work. The only downside is ammo cost and increased barrel wear (use), so if it makes you feel better, might as well do it.