Carlos Hathcock cleaned his rifles because he was a Marine.
Breaking in is advised for a new motor vehicle to allow the parts to get used to each other, smooth out various surfaces, etc., the usual procedure being to drive it around town at low speeds for a month or so, I have seen recommendations that appliances such as washing machines be allowed to "settle in". Putting 200 rounds or so through a new semiauto pistol before using it as carry gun is recommended.
Back when I read the gun magazines regularly I don't recall any of the gurus mentioning barrel break in, they emphasized tightening screws, making sure the trigger functioned properly, did not rub against the stock, perhaps allowing the barrel and action to settle in the stock, etc.