One cabinet doesn't really replace a multi-story building. Many cabinets spread out over the service area do the job. But each cabinet can perform all the functions that used to happen in the large building. They just make it economical to perform those functions for 100 - 1000 subscribers, instead of having to centralize them into a single location that serves 5,000 - 100,000.
Those cabinets are not a result of fiber. They were more a necessity of high bandwidth services without fiber. Think ADSL. Fiber actually makes it possible to go back to more centralized service while providing even more bandwidth. You can deploy passive fiber splitters in an old-fashioned pedestal and keep the active optics in the multi-story building for 100,000 subscribers again.
Maybe you meant that the active optics would only fill a small shed's worth of space in that old building. I finally caught up to you.