Redfish6 - I’ve owned literally hundreds of new barrels, from inexpensive factory tubes as chattered as a washboarded sand road to custom barrels, hand lapped as smooth as a babies bottom. As mentioned above, I generally DO break in barrels by alternating firing and cleaning every round, then every few rounds, pushing out all copper and carbon, BUT I have had enough instances where I’ve just put the rifle into service and have not seen any difference in precision; but the typical time to clean is USUALLY shortened.
It’s more accurate to say a barrel WILL break in on its own over ~150-300 rounds and will pick up a bit of speed as the bore fouls into it’s “new normal.” This CAN influence your load a bit. Not much, but enough to notice, especially if you aren’t using a velocity node based load development method. Not much, but far more change, in my experience, than the fire/clean break in process will cause.