If a particular brand of primer produce a consistent flame and everything else is also very consistent, why would pressure, burn rate, peak pressure vary?
Because at different loads/primers and different pressure curves, different things happen within the case/chamber/barrel. It's not enough to simply be consistent (because you can only be just so consistent). You also have to have the pressure curve within a regime that minimizes the effect of the inconsistencies you can't control.
This is a (rather poor) depiction of a pressure curve (pressure on vertical, time on horizontal) with a given case.
The pressure builds, then dissipates as the bullet starts to move and the powder burns itself out. A really accurate depiction would show a little bump as the bullet hits the lands and slows slightly at that moment.
The key ingredient here is powder burn rate formula - first time I ever saw this was in Jeff Siewert's book:
r=B
p^
a
where
r is the instantaneous burn rate, B is a coefficient related to the nominal powder speed (burn rate),
p is pressure and
a is a value derived from closed bomb tests on the powder - something I didn't know was a thing until a few weeks ago. Per an email exchange I had with Mr. Siewert,
a tends to be between ".65ish and roughly .83."
What's important to note here is that there is a direct, reciprocal relationship between instantaneous burn rate in the case and the pressure in the case. This means that if you spike burn rate (e.g. due to using a "hotter" primer), then you also spike pressure. This spike in pressure then reciprocates and bumps burn rate up, which bumps pressure again, etc. If you don't relieve that pressure quickly enough, you can get into a runaway condition. This is why small changes in conditions can have oversized ramifications.
So, let's take your change to magnum primers - that will definitely spike burn rate and pressure more quickly and deliver a curve that's a little more like (orange):
It will be higher (more max pressure) and narrower.
If you slow things down (e.g. using a slower-burning powder), it will be more like this (green):
Shorter and wider.
Which curve yields tighter pressure grouping when the bullets hit the lands, as an example? A small difference in time when the bullet hits the lands on the orange curve will yield larger pressure differences at that point than the same differences in time would against the green curve. Ideally, you want major events during ignition (like engaging the lands) to be taking place when differences in time deliver the lowest differences in pressure - on all these curves, that is around the apex. The lower, flatter curve (green) is most forgiving across its entire length.
If you could perfectly load everything identically the same, then in a theoretical sense the pressure curve shape wouldn't matter because you'd be moving along the same curve with every shot. But this is the real world, and you can't. So, when you spike pressure, you give yourself less latitude for error in other aspects of the load - ranging from things you can control, like powder charge, etc., to things you can't, like powder, case, and effective neck tension inconsistency.
Why would consistent primers, cases, bullets, seating depths, powder, etc. produce a "condition" to be inconsistent?
I've used various primers with the same powder load and with various powder loads and different brass and all the SD's trend to be good or decent, when uniformity of the brass and powder charges. Certainly, I get variations from one make of primer to another in velocities that effect POI. But with all the variations I've played with over the years, I've not come across an "inconsistent condition" when all the components were consistent. . . at least, not until now.
I'm in the same boat - most of the time. Most of us play in regimes where we don't have to worry about being on the steeper part of the curves (the steep slopes). We listen to others, or read reloading manuals where others have developed good loads and then we play in relatively close proximity. Making minor changes doesn't put you in a regime where other inconsistencies matter as much. This is where consistency in case prep and loading carries the day, and small changes in charge weight and burn rate (and thus, pressure) don't register as much. Engage the lands during those steeper parts, and they do.
p.s. If you haven't read Jeff Siewert's book, it's a tough read, but a good one.