.... That does however mean it would need humidity to operate... The adibiatic cooling alone would be a wash, I'm pretty sure. Perhaps differences in radiative cooling between altitudes would be a help.

But.... Even if the self powering potential is not there to maintain the chimney by itself, what's to stop us from putting 1gw of solar panels and powering the thing with fans? If the heat transfer numbers aren't wrong.... That could still be a very useful characteristic.