That construction picture of the New York Public Library was taken around 1907 and shows the exterior of the building nearly complete. There’s a crane being disassembled in the courtyard adjacent to the near corner (northeast corner of the lot, at Fifth Avenue and 42nd Street), the elevated terrace has not been started yet, and the entrance stairs for the main entrance (on Fifth) and the side entrance (on 42nd) have not been started.
This looks like a nearly-complete building, but it was still three years from opening. The interiors are both complicated and built to a high level of finish; the stacks were a huge puzzle to be assembled, and moving the books, manuscripts, and other documents from the three libraries that were being merged to form the NYPL must have been a huge task in itself.
Here’s a view from the southeast a bit later:
The terrace has been built and the front steps have been built, but we still have two small cranes (one on 41st Street and one on Fifth Avenue just south of 42nd Street) working away. The short version is that a large, spatially complex building with an ornate stone exterior, and with stone, ornamental plaster, and ornamental wood interiors took time to build then and would take time to build now. The fact that the exterior was enclosed in 1907 didn’t actually mean that the work was almost done.