Getting dressed for work before 1930 was a daunting prospect. Studs and buttons. Sock garters and trouser braces. Collars and cuffs. Ties to tie and cravats to fuss over. Stick pins and pocket squares... and that's just for men!
Here's a delightful selection of cuffs I've owned. One attached these cuffs by using one or two buttons or a cufflink to the shirtsleeves. As detachable cuffs tended to move around a lot you could then attach a 'cuff holder' which is a spring loaded metal gizmo to stabilize this movement.
The reason behind having detachable cuffs (and collars) was that these were the areas that wore out or were soiled first. By replacing the cuffs and collars, rather than the whole shirt, you could extend its life considerably. Yes, our forefathers knew how to economize.
By the 1940s nearly all shirts came with attached collars and cuffs. While some makers were still manufacturing detachable cuffs and collars into the 1950s, by the 1960s they were a relic of a bygone age.