My understanding is that, yes, it is possible, but the engineering gets crazy. The elevator issue is just one problem. Another is the piping and wiring you need. Then you get into the structure itself. How thich and how strong does it have to be to support its own weight to those heights. Even if the walls were paper thin, a mile of paper weighs a lot. The HVAC issues are another big deal. Imagine the cooling towers to keep that place cool.