I imagine you'll get answers that vary from one end to the other of the entire range...
For me, it depends on the rifle. .22LR I clean when the action gets dirty or accuracy starts falling off. For the more accurate center fire rifles I have, I clean like you do, then let them sit over night after running a patch soaked with Hoppes #9, then run a couple of dry patches followed by a bore preservative before storing. For the plinkers & less accurate center fire rifles, I rarely go the full distance with copper removal, and never worry about the last overnight soak with Hoppes #9.
No, removing the last bit of copper does not take the barrel back to "pre-seasoned condition". Barrel seasoning / break-in smooths out some of the the microscopic imperfections in the barrel, forever changing the surface.
Certainly, for many firearms that "squeaky clean" barrel needs a bit of fouling before it settles down to shooting good groups. Some only need a couple of rounds, others might need more (or less, I suppose, but I've never owned one that didn't benefit from a couple of fouling shots.)
The barrel is clean when you say it is. For me, I don't want to spend forever cleaning up, I want to spend more time shooting and less time cleaning. Others find their happy place with more or less cleaning. Find yours and don't worry about it afterward.
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Just a Shooter