The break-in procedures I've seen involve making sure that there's no metal fouling buildup so that each round goes down a completely clean bore. The direct contact between the bullet and the bore is supposed to gradually smooth the bore. A smoother bore will tend to foul less and that will tend to contribute to better accuracy over time.
Cleaning very often, maybe after every single shot initially, will insure that it's easy to remove all the fouling and insures that every bullet contacts the bore instead of potentially riding down the bore on a thin layer of fouling.
So what's my take?
Did you buy a custom barrel with a properly lapped bore? Then you shouldn't need to smooth it out.
Ok, so you bought an off-the-rack, production rifle. Let's assume that we agree with the idea that copper jacketed bullets going down a completely clean steel bore will smooth it out significantly. There are decent arguments both ways, but let's forget about them and just accept this as fact for the moment.
The basic idea is that you want bullets in direct contact with the bore to do the work of smoothing. The break-in procedures generally involve firing a round, cleaning, firing a round, cleaning...at some point you fire 5 rounds and then clean, repeat that a time or two, maybe increasing the number of rounds again and repeating that until finally you're done.
Are you going to take your rifle to the range and shoot maybe 20 or 30 rounds in a day? Then don't bother with break-in. INSTEAD, especially when the rifle is relatively new, just make sure that you clean the bore back to bare metal after every trip to the range. Remove ALL metal and carbon fouling from the bore after every range trip. Most people don't do that. It will take more effort than a normal cleaning and will involve some sort of method to actually remove copper. Bore brushes, patches and typical nitro solvent won't usually do much to remove metal fouling.
So maybe it takes you longer to get the bore broken in because you're shooting more rounds between each of the rounds that goes down the barrel touching bare metal. What does that hurt? Unless you have a bore that's really rough, or unless you need to shoot a large number of rounds in a single range trip without any accuracy loss at all, it won't hurt anything.
Eventually, over the course of a number of range trips, you will have achieved exactly the same effect that the break-in procedure would have. But you never had to do anything other than clean the bore thoroughly after every range trip. Admittedly, most people probably don't remove all the metal fouling every time they clean a rifle bore, so the cleanings you do will be more work than normal, at least at first.
The exception might be if you are involved in competition or some other shooting endeavor that requires a relatively large number of rounds fired at a single range trip. Especially when it is unacceptable to have an accuracy drop-off due to metal fouling buildup during the course of firing those rounds. If that's the case, it might make sense to take steps to smooth your bore with a break-in procedure.
Or you could just have a good gunsmith lap your bore.
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