Elevators are counterbalanced -- when they are going down, there is a counterweight going up. So there's less energy than you might imagine being generated.
Having lived in a 17-story building with Thyssen-Krupp "green elevators", they're terrible! An elevator would break down and require days of maintenance every couple months, greatly increasing queueing times.
When it does, you might be able to use it to generate electricity. But I wouldn't be surprised if that isn't done simply because it wouldn't justify the added cost and complexity of building all that extra energy harvesting mechanism into the elevator.