Conventional wisdom has always said clean from the breach if possible to avoid wear at the muzzle crown.
Obviously not possible on some guns.

I seldom remove a brush. I pull them back through. Sometimes, I pull them back without exiting so the bristles are pointed toward the direction of travel. That's rough on brushes, but it is also rough on rust and leading. Brushes are cheap.
If I'm pushing lots of soaked-loose crud out, I'll remove a patch often, and sometimes a brush.

Go back farther and read Townsend Whelen- "Mr. Rifleman".
Whelen said "Only accurate rifles are interesting."
He was going to have a pet rifle shortened, so he headed to the range with rifle, pet load ammo, and a rat tail file.
He fired a control group for baseline accuracy.
Then, he mutilated the bore on one side of the muzzle with the file.
No change in groups.
Then, he made more pronounced mutilations.
No change.
He went on to make it practically a blunderbuss with no appreciable change in groups.
Don't believe me. Read it. Read about Whelen. One of the first men to ever shoot the 1903......

YMMV.

__________________
Regards,
Lee Jarrett