If I were to measure any one thing on rimfire ammo, it would be from the top of the rim to the leading edge of the driving band.
Measuring only rim thickness ignores important details like
where the variation in the rim thickness is in relation to overall brass length as well ignoring bullet seating depth. Who cares how consistent the rim thickness is if your bullet depth is all over the place.
Measuring from the top of the rim to the driving band of the bullet will enable you to be consistent in bullet placement when chambered; whether it's how much of a jump you have or how much contact with the lands there will be, because then the variations of the brass length or rim thickness won't matter in the grand scheme of things. You know the key metric is where the bullet is in that barrel. Measuring in this manner will show that rim thickness varies
outside of the chamber and could possibly impact ignition by being farther from the barrel and being striked by the firing pin sooner, but I doubt it would be enough to ever be measurable in performance or possibly even lock time.
Recording rim thickness or OAL or weight or most any single measurement on rimfire ammo ignores too many other aspects of the cartridge you would also have to measure to provide context to your original measurement.
If the rim thickness varies...ok...what does that variation impact? Did the location of the leading edge change? Was the the base that changed? Was it both? Something else you'd have to measure.
Weight changes...ok...was is brass density? Lead density? Power variation? Primer variation? Lube amount? Who knows if you can't measure it all separately.
OAL varies....ok...so the tip of the bullet isn't in the riflings so you'll have to see where the driving band is in relation to the bullet tip and what if the rim thickness isn't consistent so you'll measure rim thickness to see where the variation is OAL is.
Trying to control the variables in factory loaded ammunition is a rabbit hole you don't really come out of because you would have to disassemble each round to properly find the individual measurements that we can and do with hand loaded centerfire ammo.
In the game of silhouette, I personally think what accuracy improvements that can be gleaned from measuring ammo (outside of lot testing) isn't really score impacting so I don't currently measure anything because like you asked, I don't think it's worth the trouble. That and I think the ammo Lapua/SK/Eley is producing these days is great and doesn't require such tedious activities. Maybe if you're trying to get all you can from some cheap ammo you just want to burn up, but if I were to measure anything, it would be the leading edge of the rim to the leading edge of the driving band to ensure the bullet is seating consistently.