The application of this is not in energy production or - realistically - CO2 capture on a global scale. This takes huge amounts of energy to do and requires a sophisticated chemical synthesis in the background in order to replenish the catalyst.
Pretty much the only reason to do this would be because you're specifically interested in generating propane. For example, it could be very useful for ISRU on other planets, or to generate propane "for free" from a solar setup.
If your goal is energy production, you'd just use the output of solar panels directly without this costly step in the middle. If you want to store energy locally, electrolyzing water into H and O would be hugely more cost effective. But propane is a more dense fuel that would be useful for mobile applications such as ships and cars, and can also be used as a raw material in chemical synthesis.
Pretty much the only reason to do this would be because you're specifically interested in generating propane. For example, it could be very useful for ISRU on other planets, or to generate propane "for free" from a solar setup.
If your goal is energy production, you'd just use the output of solar panels directly without this costly step in the middle. If you want to store energy locally, electrolyzing water into H and O would be hugely more cost effective. But propane is a more dense fuel that would be useful for mobile applications such as ships and cars, and can also be used as a raw material in chemical synthesis.