It depends.
If it's factory new ammo of the kind you usually see in big box stores, most popular brands will shoot well enough where you will not notice a practical difference at 7 yards ( about your distance) versus premium ammo.
However that is assuming: your gun doesn't dislike that ammo for whatever reason. That's why I said factory ammo. Winchester white box, blazer, PMC, wolf, Tula, s&B, all those typically do about the same in my guns at 7 yards or less.
However sometimes you will get a gun like one of mine: an out of production Italian service pistol made in the 80's that does not group well with FMJ and only shoots well with lead bullets with a long bearing surface. So when we talk about hand loading or reloading ammo, then variables like powder selection, powder charge, bullet weight, and burn rate have the potential to create a mismatch with a given pistol.
In general premium self defense rounds are supposedly held to tighter standards with regards to bullet weight, shape/size consistency and powder charge so they are thought to produce more consistent groups at 25 yards than practice ammo if the shooter is up to the task. you will see people post their best group of several for the day and usually it will be around 4 inches on up (remember most groups are bigger or they wouldn't bother showing the small one), sometimes 2 or so with Luck and a customized pistol (and a rest, maybe a scope) My eyes won't really allow for that. And with gun magazines sometimes they will use a ransom rest and their group sizes are miraculously small. So don't get hung up on group size at 25 yards unless you want to be.
I would agree with your variables but exceptions/lemons don't follow a ranking order. I'd also create another category and that is whether the gun (mostly bore diameter) prefers a given load regardless of level of quality of that ammo. An expensive undersized copper jacket hollow point bullet would not do as well as a slightly oversized lead projecticle all things else being equal. If your gun loves the reloads - great! I wouldn't hesitate to try a couple other brands though and actually measure group size since For side by side comparisons. This is after someone has their fundamentals down well enough to be a consistent shooter otherwise how do you know it's the ammo and not you? An instructor or very experienced friend (who has good fundamentals) can test fire a few rounds to compare.
In most cases ammo is not responsible for shots low and to the left or low and to the right for lefties. Nor is it for shots way low at 7 yards.