I think it's pretty well debunked.
This is easy to say, but you've provided exactly zero evidence.
Consistency is what matters.
Absolutely. And some cartridge designs are more consistent than others.
If it does exist, it's so incredibly small of a factor, relative to other factors, that no one ought to worry about it or focus on it.
Nobody should except serious target shooters. Again the difference in accuracy due to cartridge design is small enough that you can ignore it in a hunting weight sporter. It's big enough that serious benchrest shooters can't ignore it.
Sure the 6mm PPC has won a lot of 300 yard matches, but the .30-'06 has won a lot of 1k yard matches too, and it's not considered an intrinsically accurate round.
I'm afraid you've contradicted yourself. If the 30-06 is not considered an intrinsically accurate round, then the there must be other rounds that
are considered intrinsically accurate. Which there are.
The 30-06 may have won lots of long distance matches, but I suspect that that's because it was the standard military cartridge at the time. What was the hot ticket
at one time isn't the point. The point is that if cartridge design didn't make a difference, then serious target shooters would be using random cartridges. You'd look at a benchrest contest and there would be shooters using 222, 223, 222 Rem Mag, a whole slew of cartridges. Yet almost all shooters tend to use the same cartridge for a given discipline,
because cartridge design makes a difference.