I am a big fan of John Barsness & find him extremely practical & knowledgeable. He does not find any benefit in breaking in a new barrel.

I have had some new barrels & rifles and read up a lot of advise. My conclusion is as follows

1 Cleaning a new barrel or rifle is a CRITICAL issues. The barrel & action will have grease, oil, preservative, varnish etc. It will also have saw dust, metal filings, spurs & other rubbish from the factory or gunsmith's workshop. The bolt lug recess will hold such dirt. So I ALWAYS give a new barrel / rifle a good squirt of degreaser. It is surprising to see the amount of solid rubbish that comes out! Then I use a flexible chamber brush (a wonderful tool that I have seen only once in a shop in New Zealand & bought it) & scrub the chamber & the lug recess of the action & give another squirt of degreaser. Some more rubbish can be seen on the towel on the floor. Then I use a soft cloth & try to reach all the corners of the lug recess, even using a bamboo kaba skewer to get to the corners. More solid rubbish can be seen on the cloth. I then use solvent to clean the barrel in the usual way. Scrub with a wet patch & dry out with a few clean patches. If I am not shooting the rifle immediately, I use Break Free CLP & give the rifle a good wipe inside & out.
2 The breaking in of a new barrel is another issue all together - I now just shoot the rifle normally - 10 to 40 rounds at the range. Come home & clean it. I use JB paste to scrub the stainless barrel - this certainly smoothens out the tool marks & sharp edges (a Barsness recommendation). I almost NEVER use amonia based solvent (Sweets etc) anymore. In my early days of ignorance I stupidly left Sweets in the barrel of my Tikka 222 overnight & it looks like sand papaer now. Fortunately the rifle still shoots 0.5" groups with 5 shots! The only exception is when cleaning after using the old barnes X bullets as the fouling is terrible. On such rare occasions I use a strong solvent & wipe it out in 5 minutes & follow up with normal solvent or Break Free. The TSX is a real dream & does not foul barrels any more than lead core bullets.