This is actually a very old idea...
This was in a sci-fi story 'Waaaayy back there somewhere -- but in the story, the "towers" were actually helium-levitated tubes of plastic floated over a horizontally-spinning turbine at the bottom.
They were meant to channel heated ground air up from the solar-heated prairie, which would, as in this design, generate its own pull on the way up.
But in point of fact, such a design would not work, simply because the air outside the tube would rise faster than the air inside of it, due to the tube's constriction. Thus a tube would never get the flow started in the first place.
The missing piece that makes this design work, is the large solar heating space at the bottom. That should generate enough heat to get the flow started up the tube.
What can I say? Sci-Fi doesn't ALWAYS anticipate actual science.
But note: I still see no reason why a flexible, dirigible-floated tube wouldn't work perfectly well for this design; and that adaptation might save these builders a LOT of money.
