I see big changes with primers as a causing or clearing of powder ignition issues.
Powder burn is nowhere near linear to begin, and then various bullet:capacity combinations shape the burn in unpredictable ways. This kind of stuff could be seen with pressure trace, but always has to be measured across a chrono and targets before decisions could be made.
Another factor in the mix with different primers is the striking of them. No doubt a fixed striking would favor one primer over another -until optimized for the other. I suspect nearly any primer could provide best results with striking specifically tuned for it. Start swapping primers and striking tune could collapse or improve.
So why do we trial & error primer swapping, and not adjust striking for the best in each before deciding? I imagine it's because doing so is difficult and costs barrel life. But if you intend to stay the course with a gun, across multiple barrels, this is worthy of consideration. After all, once a primer at set striking is proving best, there may not ever be a reason to fiddle with it again.
I had the misfortune of a firing pin set screw slipping. This opened my accuracy with seemingly continuous flyers. ES jumped beyond 50fps. Yet every primer fired, so this was very difficult to isolate, and even more difficult to recover from. Once I finally figured it out, I had to re-tune the gun with no more than firing pin settings.
Anyway, it worked. I could come in & out of best tune with this adjustment alone. In the end I cut another 1/8th moa over prior best. This, taking me from 3/8moa grouping to 300, down to solid 1/4, which is huge! That took a day at the range with one chosen primer(a worthwhile day).
I wish I could explore it enough to define as a standard, but I'm just a working dog, and cannot afford the endeavor.
Keep it in mind though. A primer/ignition problem might not actually be the primer itself,, and it might be an opportunity.
