I do not have enough experience with brand new bores to say one way or the other. A brand new Ruger #1 got the "series" - clean with Butch's Bore Shine until no colour on the patch. Fire once. Clean until no colour. Repeated 5 times I think? Then went to two shots between cleaning. After 10 or 12 rounds, either I was getting more proficient or something was occurring, many times first patch came out with colour, second one was white. Most bores I get here are used - some take weeks of soak and scrub and various cleaners - especially 100 year old milsurps - some I actually do eventually get clean so that no colour anymore on the patch. But I can not comment whether that "break in" series does anything to make that barrel most accurate or not - I can not even imagine how to prove that one way or the other. I had read from guys like John Barsness that he cleans when new, fires for a box or so, until accuracy starts to drop off, then gets at the cleaning again. I do think there is a relationship between "clean" and tighter grouping, but can not say that a particular barrel is more or less accurate due to the "break in" procedure. As well, Barsness has mentioned several times about a heavy barrel Remington 700 he shoots - described it as most accurate rifle he has - regularly goes past 200 rounds before seeing a drop in accuracy, so that is when it gets the bore cleaned. Must be a very good barrel.
For some of my acquaintances, I suspect the "break in" gets lost in the iffy bedding, iffy scope, iffy scope mounting and so on. I suspect "breaking in" is something they understand to do, and so must be a good thing to do...