Paul, your comments seem to support what I would expect to be a common approach, that tracking larger numbers is more a subtractive process. i.e., you order 300 chicks, they arrive and you verify you received 300 chicks, over the next several weeks in the brooder you lose 3, so you're at 297.
When they go from brooder to coop, it is a chance for an accurate count - hopefully 297 and you did not have more losses that you never saw evidence of (?!).
And from there on, for the most part it's a matter of subtracting when you find a dead chicken, and keeping a tally that way, until with the broilers it is processing time and of
course you get an accurate count there.
And with a laying flock, you might add x many every couple of years and cull y many every couple of years and you would have good numbers on how many you put out there and how many you culled, but if a predator grabs one or two and makes off with them now and then, unless they leave the bodies where you find them, they might not be accounted for.