I've learned that about 14 days (2 ounces), hens are ready for chicks to leave the nest and follow them into the flock to feed. Typically, they chase their chicks away at 5-1/2 weeks (15 ounces). That sounds like the age when we used to put machine-hatched chicks out on the range.
Apparently, removing chicks early can ensure tameness. Some hens hang onto them for months. Another reason to separate chicks would be to sell them. Smaller birds are cheaper to sell and ship.
Going into a flock to grab certain birds can be a hassle. Chicks could be injured. The excitement could impact egg production. Mother hens can be aggressive. The practice could result in a wilder, harder-to-manage flock.
I don't know how farmers separated chicks in the days before mechanical incubation. If the flock was used to going through an opening, an adjustable temporary panel may have been just what a farmer needed for removing chicks without upsetting the flock. Where's my 1900 Sears Catalog!