The best barrel made fit to a receiver whose face isn't squared up with the chamber/bore axis will walk its shots as it heats up. As the metal expands, the point around the barrel shoulder that bears hardest against the receiver face has a stress line at that point. It makes the barrel axis bend a little bit in one direction. Very typical of commercial rifles. It would add $50 to the price of the rifle if they squared up their receiver faces, but it's not done. I think Savage's better rifles probably have their receiver faces most square with the barrel bore/thread axis. One reason they do well in matches.
If the receiver face is squared up, most barrels will shoot to point of aim starting out clean and cold to dirty and hot over several dozen shots. If a barrel doesn't do that, it's not properly stress relieved. Muzzle velocity may increase a dozen or so fps as the barrel's fouled, but it stays there for many shots. Best proved by a clean barrel shooting 40 shots about 15 to 20 seconds apart and all landing inside 2 inches; at 600 yards.
Ask your local 'smith what he would charge to face your favorite rifle's receiver, then shim it so the barrel would clock in for correct headspace and sight alignment to the vertical plane. If there's no sights on the barrel, it could be shimmed so its headspace would be at minimum for best accuracy and case life. Who cares if the stamped info on its left side gets turned under the barrel in the stock's fore end?