For two different points of view,try the sticky post here "The Wisdom of Gale McMillan"
And then go to Kreiger barrels and read about break in.
Lets differentiate between production barrels and premium,hand lapped barrels.
There is NOTHING the shooter can do to improve the best efforts of a premium barrelmaker.
To the actual workof the barrelmaker,I say "Just shoot it"
However:The barrel maker,hopefully,has all of the "lines",the texture,in the long direction of the barrel.(Not so much on production barrels).
The issue is in chambering.Thats usually outside the barrel makers hands.
We will get SOME degree of cutter marks,burrs,mismatch,and other imperfection from twisting a chamber reamer in.
A very good job can be done!.Sharp reamer,fitted pilot,gunsmith skill!! It can be 99% perfect.But no one can go in and deburr the downstream side burr on the edge of a land.Even the sharpest cutter leaves a burr on an interrupted cut.Maybe a very small one,but its there.
Those imperfections CAN cut,and litter the bore with bullet jacket flakes.
Those burrs can be worn off with a few rounds of shooting.
I don't think it crazy to wipe metal chips out of the bore before shooting another bullet over them,smearing or impressing them into the bore.I'm talking maybe a wet patch and a couple dry patches.
And in case you think softer copper cannot hurt harder steel,I worked for many years with plastic injection molds.
P-20 pre hard mold steel or DME #2 Mold plate steel are not that different than 4130-4140 sort od steels they make barrels out of.
If your mold or process leaves plastic flakes,drool,etc on the parting line,when the mold machine clamps up,even polyethylene or santoprene can leave an impression,a dent,in the mold faces.
IMO,a 'break in" bore wiping is NOT about "Improving" the work of the barrel maker.Its about protecting the bore from damage running bullets over jacket flakes.
Now,a "Midells" or "Brownway" $127.00 pre-threaded,short chambered barrel"
or a Remchester,or ? just MIGHT look like power feed tool marks or galled,smeared cheese from the button or?.And any "texture" that's crossing the path of the bullet will foul.Bore cleaning between shots won't help much.
I actually have had surprising success with a "nothing to lose" substandard barrel via my own firelapping process.It was a 30 cal bbl.I used 170 gr cast 30-30 bullets. I filled the lube grooves and charged the OD with the green #9 diamond mold polishing compound. I can look up the micron size.Its quite fine.
After about 20of those,modest loads,with a lightly wet bore,that rifle shot surprisingly well.
My hint with firelapping? FORGET progressive grits.The big rocks cut more clearance,or a larger hole.
And you don't sand 80 grit marks out of a board with 400 grit going the same direction.You have to cross the lines.
IMO,you only do this to an otherwise poor barrel,out of a "nothing to lose" experiment.