Yeah, but there's power and there's "power."

Know those semi-worthless solar chargers you can take camping? They've got a goofy little flashlight and a USB port and if you let them sit all afternoon they'll charge your iPhone like 4%? As chargers, they suck. As flashlights, they suck. As pack objects, But as something that will get your GPS up and running again if you're lost on a mountaintop, they're pretty damn badass.

Presume your solar synfuel recracker operates at one tenth the efficiency of a refinery. Hit that refinery with a carbon tax that reflects the externalities of their environmental damage, then allow them to defray that cost by paying for direct solar recracking. It will always do a worse job than planting trees, but places we need to plant trees are often places we need to send troops and something like this promotes local industry.

Magic bullet? No. Reasonable technology to pursue? Yes. Any commercial economy is going to leverage a whole lot more from building gadgets than from planting trees, especially as we tend to cut ours down for lumber.