Because, in the original installation, the elevator machines were at the bottom. That's rare today, but in 1907, getting the heavy machinery up to the top of the building was much harder. Some old elevators have a winding drum at the bottom, and this was apparently one of them. So there was too much wire rope and pulleys involved.
Getting the new machinery up to the top was a miserable job. The article hints at this. "The Metropolis Trust Building is located on one of the busiest corners in San Francisco; so there was no chance to use cranes. And the building itself offered limited access; there was no loading dock or service entrance. All equipment had to enter through the front door – including 20’ pieces of reinforcing steel and 4,000 lb gearless hoist machines." They had to remove two elevators and cabs to get an empty hoistway so they could lift all that stuff. They had to get lifting equipment up to the top. They had an existing elevator to help, but they still had to move stuff from the top elevator stop to the top machine room above, somehow. This brings up images of a lot of big guys, chain falls, small electric hoists carried into position by hand to move larger electric hoists, and lots of temporary steel beams and timber baulks. This was probably night work, because all this blocked the building entrance and lobby. They got a 20 foot steel beam in the front door, into an elevator shaft, hauled it up to the top, got it out, raised it one more floor, and put it into position. That was just a small part of the job.
That's why nobody replaced the machinery for 110 years. It's also why elevator mechanics are one of the highest paid trades.
They put in a modern gearless traction elevator machine, which is mostly a big motor directly connected to a big pulley. The mechanical part is far simpler now. The controls shrink, too. The old AC-DC motor generator set gets replaced by a box of high-powered semiconductors about a cubic foot in size. The big relay panels get replaced by a microprocessor control box. This is just a 15 story building, so those are all standard components.
Too bad there's no video. Star Elevator did post a video of another job at the Oakland Tribune.[1] That didn't have the access problem from hell.
I understand the machines were in the basement, I don't understand why the motor for 2 was under shaft 1, 3 under 2, and 1 under 3.