Why don’t the engineers just use magnetic levitation for elevators?
http://www.toshiba-elevator.co.jp/elv/infoeng/technology/tec05.jsp
Toshiba has developed a permanent magnet/electromagnet method to keep the elevator from touching the guide rails. It has nothing to do with vertical levitation.
I vote we fall back on "Beam me up, Scotty."
Because magnetic levitation of significant weight is measured in inches (or fractions of an inch), not hundreds of feet.
If it was made strong enough to lift an elevator full of people, it would rip every ferrous metal object off of you and hold it on the ceiling. A little bit of steel in your zipper would shred your pants as it zipped past your nose.