This is wrong, or perhaps I misundertand.
Entropy is a different concept from economic viability.
The rule of non-decreasing entropy applies to closed systems.
A carbon capture system running on solar energy on Earth (note: wind energy is converted solar energy) is not a closed system from the Earth perspective - its energy arrives from outside. It can decrease entropy on Earth. Whether it's economically viable - totally different issue.
...and I don't think the Sun gets any worse from us capturing some rays.