I have nothing but respect for what Carbon Engineering has done. In many ways, they opened people's eyes to what's possible when it comes to direct air carbon capture. The more people doing carbon capture, the better - we have 1T tons of CO2 to capture, and we need as many shots on goal as possible to get there!
That said, this is a really great idea, as heat pumps will be increasingly used for all sorts of temperature management. Cutting 10% off of costs by using somebody else's fans could be great, as long as hauling the CO2 filters off and replacing them is cheap.
That said, OP's idea does have merit. avernon, I think you hit the nail on the head with your comment downthread regarding the main concern being avoiding disruption to existing plant processes where this kind of tech might be installed - I would be worried specifically about how radically raising the pH of cooling process water would affect mineral deposition, for example, but then that in turn would surely depend on how a given plant had set up its cooling system to begin with.
Nevertheless, it seems very likely that this idea could in itself knock about $4/t off of the cost of CO2 relative to the CE estimate ($212M saved for their air contactor design amortized over 30Mt of CO2 captured during a CE plant lifetime) which in the best case is around 5% of the cost of the CO2 capture.
Plus many facilities have surplus low pressure steam you could use to regenerate your fluid.
And then you two guys come in with the idea that in hindsight seems completely obvious, use all the cooling towers already out there! The most start up thing ever.
I used to be an engineer at an ammonia plant. Many of them already capture and sell CO2 from their process. So they have the infrastructure to compress and sell CO2 already on site. The plant I worked at was in Augusta, GA. Might be worth checking out ammonia plants as a growth market.