A count? No idea. I was taught this way by the 'smith I worked under back in '92. Since then, I've spun a "a couple" barrels.
You don't have to do it., if you don't believe in it. I'm not offended. Really. You believe in your way, I believe in mine. It's your gun. You do you, I'll do me. I was answering the direct question of the OP of my thoughts and my steps. Plain and simple. IMO, a "waste of ammo" is when you blast away and don't learn anything from it.
So exactly what have you learned from almost 30 years of fucking around with cleaning a bunch at the range? Apparently not that barrels are broken in by bullets passing down them, not jags and brushes with solvent and that it also takes a lot more than a typical 20-30rd break in procedure to accomplish that.
A high quality hand lapped barrel usually takes 150-250 rounds to be broken in. A shitty rough factory barrel like a Remington, Savage, etc I’ve had take as much as 500 rounds before they settled in. Cleaning does not accelerate the process. I’ve broken in a crap load of barrels and used to do the lengthy procedures and one day said fuck this shit and just started shooting them and what I learned is that I wasted a lot of time and effort for nothing.
The only thing I’ve seen that helps break in is the Tubbs stuff. I’ve ran the final finish on several stubborn factory barrels and it worked. I also played around with the throat maintenance bullets on a few Bartlein 6mm barrels and they seemed like they might have done something shooting a few first, then shooting a few more after 50 rounds but they all still took about 150 to break in which I guess is on the low end for what I’ve usually seen from good barrels, but that’s not definitive for me. If the barrels picked up speed and stopped copper fouling entirely after the first 50 rounds and then never picked up speed again I’d be somewhat convinced but that’s not what happened so I’m not. They are great at eliminating carbon rings though. I smoked out all 3 of those barrels running H4350 and would do a light cleaning, run two throat maintenance bullets, and light clean again and did this every 300 rounds and I never got a carbon ring in any of them.