I think there are really two major business cases for Prometheus. One is in earning back carbon offsets (reducing net CO2 production from a polluting source) while producing a valuable byproduct. The other is as a way to ethically and profitably use local excess energy to create that same byproduct.
I think it makes sense for the Prometheus apparatus to be paired with electrical load balancers (aka industrial battery banks) built for renewable energy. Allow me to expand:
1. Renewable sources like solar collect electric energy on an inconsistent basis.
2. Depending on local energy demands (a factory, the neighboring town, etc.), the grid will either use or store the electric energy. Storage for large businesses and nations nowadays occurs through industrial battery banks (i.e. BYD's).
3. Usually, those who use battery capacity battery stored energy can be used before conditions are right for collection again. However, if local energy demands less than can be stored and used in the next collection cycle, that "buffered" energy is wasted.
This is a prime use for that wasted energy. I imagine it only becomes viable at scale. And there is one other issue to address...
Companies like BYD who do national-scale renewable grid storage usually undershoot the amount of battery storage they provide because over-storing is costly (the energy isn't used or is distributed less efficiently and the batteries incur both capital, installation, and maintenance costs).
If Prometheus reaches cost effectiveness, a renewables/storage company could start over-providing energy generation and battery storage and pair it with CO2 factoring to a) reduce costs associated with wasted energy b) earn carbon offsets for large companies and c) create valuable byproducts.
Likewise, batteries/capacitors/whatever would probably be set up on the electricity. A plant design would seem to want to control the flow rates of both.
Overall, the parent comment's unlikely to be correct in its speculation that the reason for open-air capture is related to timing issues.
I suspect the advantage of this system is that is doesn't need pure co2 to work
edit: You'd probably want to store the electricity on-site instead for this. At least if there's no CO2 to consume you can be in the electricity storage business.
The process uses clean electricity to reverse the CO2. I suspect here we have a timing issue. When the sun shines, the gas plant will be idle, and that's when the spare electricity is available is used to reverse the process.
And the physical position - the gas plant is likely to be where the sun shines less.
As ever we have a storage buffer problem.