Solar Updraft Tower as Antenna Tower

There seems to be a trend involving ever taller structures these days: Tokyo Sky Tree etc..

If it's apparently economically feasible to build a tower only to put an observation deck and antennae on it, then why not use the tower itself to generate electricity (because it's already there), simply by lining it with a tube. The added expense to build a tube up the middle wouldn't be that much and convection would create a natural updraft through the very tall tube, which could spin turbines and create (some) electricity.

One big drawback is the land area needed at the base for the collector, but this assumes that we are making an actual industrial powerstation rather than just powering the single tower itself. The suns rays could be focused (perhaps with shiny surfaces) around the smaller base to heat the air enough to rise through the middle of the tower.