Thinking back to various bits and pieces of reading through a long, long time: The first shots will burnish a barrel. Same as piston rings in the cylinder of a car's motor. PHil Sharpe and others, back in the 1930s, mentioned lapping a barrel by using only lead bullets for some number of shots.
When McMillan spoke of the perfect barrel, he was including the idea that the diameter be uniform throughout its length, as well as having as polished a surface as possible. Note that the quality of machine tools is much higher now than in the 1930s--or at least such machine tools are available if one pays the cost.
The fact that a barrel "is easier to clean" means that burnishing did occur, making a smoother surface. That indicates a less-than-perfect barrel at the start, which is to be expected at the price of a Remchester, etc. Whether or not the barrel is more accurate than otherwise is problematic. I don't believe one could take two barrels from the same manufacturer and do a break-in on one and not the other and have a valid comparison test for accuracy. 100 of each, maybe. Maybe.
I've just seen too many 1/2 MOA groups from rifles of mine, my father's and my uncle's, going back before 1950, to have any worries about "break-in".
Art