I think the important thing to remember is that early elevators were heavy machinery used primarily for industry. Think large steam-powered things. The first Elevator Union in the US was for Elevator Constructors, not simply operators. The change of elevator operation from an industrial job to a hospitality job follows the improvements in technology that allowed automating the complex and sometimes dangerous mechanisms of an elevator.

Deaths in early elevators due to people falling down shafts or being crushed or caught between the floors and elevator carriage made having a properly trained operator desirable.

It took some time to really create a fully automated system usable even by children. Early elevators would have an operator control a lever to stop the elevator properly level with the floor and operate the doors. This required training, and as technology improved building and business owners would add other services that operators provided so they became a part of the service and hospitality industry. Things like making announcements, escorting guests, and delivering mail.

Have a look at:Elevator Systems of the Eiffel Tower, 1889, by Robert M. Vogel, it has lots of nice pictures that show the complexities of elevators at the time.

There's also The History of the American Elevator Industry 1850-2001(pdf) that may be interesting to you.

Because the automatic elevator was only invented in the 1930s. They didn't become common until after the war, as buildings were built with them.

Elevator operators hadto be able to smoothly bring a car level with the floor, without jittering up and down, or leaving a drop-off to the floor or a ledge to catch the toe and trip the person. This took skill and practice.

Follow up question, what happened to the elevator Union?