I never heard of breaking in a barrel until I came onto TFL. I just tweaked the bedding of the stock, and tailored my handloads until I got around 1/2 MOA and thought that was good enough.
As for .22, the low velocities don't really wear anything. And, the soft lead does some burnishing over many thousands of rounds, but I doubt that the "break-in" process you describe would accomplish much.
As for cleaning, quality ammo leaves little residue which won't be removed by a slightly oily patch. Unless there is a humidity problem in your local area, it's hardly worth bothering with, other than on a J. Random Occasional basis. Since powder residue *is* mildly hygroscopic, wiping down the bore never hurts, of course.
Lemme put it this way: In the last 55 years or so, I've never had rust in the bore of any of my .22s (or any other rifle, pistol or shotgun, for that matter). One of them is an old WW II Mauser training rifle.
FWIW, Art