Way back in the 60's,folks figured out that soft cleaning rods,like brass and aluminum,were hard on barrels because microgrit embeds in the softer metal like a file tooth.Always in the softer material.
I want a hardened(I'd prefer nitride hard) one piece,straight rigid,polished cleaning rod.Harder than barrel steel.
Using a bore guide minimizes friction.But what is best?
Like barrel break-in (or not), and a gazillion other topics- particularly related to handloading- there's no "right" or "wrong". Each has it's advantage, and disadvantage.
I suspect your preference(though being unconventional- I've not read of any empirical evidence), being of harder material, risks "damage" to the throat and rifling given it's hardness . No matter how hard or stiff- seems there would be risk of contact with the leade (as you state, if a bore guide is used as it should there would be no contact with the leade) , and flex pushing a tight patch down a long tube would contact the rifling.
Vinyl coated rods- like the Dewey's I use- can do exactly what you mention, collect grit and act like an abrasive when in contact with the rifling. Best to just replace them every so often to mimimize that risk.
You present an interesting theory with a hardened rod- but seems that if that were preferable, we'd see them being used by BR shooters and available commercially. Perhaps they are- and if so I'd be interested in taking a look.
Minimizing the number of strokes- bingo. No one can argue with that logic.
For me, I don't even use brushes because I don't like them. Wipe-Out foam, and patches. Nothing wrong with the correct brushes, just my preference. But using them incorrectly (which I see frequently at the range) by running them out- then pulling them over the crown and back into the bore is a no-no.
Anyway, back OT- since the OP says his smith borescoped it, and says it's copper; and the OP says he can
see the copper streaks sounds like that's certainly the issue to be addressed first. KG sent me KG-12 to test out, but I've been so "sold" on Wipe-Out for many years I haven't tried it yet, but need to.