In AZ and likely Texas, they could be powered by clean energy. They’re not, but they could. AZ can produce an insane amount of solar, and sun farms are continuing to grow. Texas can produce a hell of a lot of wind power if they could quit arguing against themselves. AZ also has some hydro from Hoover, and a nuclear plant.

There’s just a hell of a lot more effective steps we could be doing before trying to get to these capture systems. And even if the capture works and completely offsets the carbon used to build the systems and the power used to run them and 100x more, it’ll just be used as further excuse to continue to do nothing.

Reading your comment makes this concept even stranger because you can sustainably farm trees to get the same carbon removal benefits and then also make money selling the lumber which will keep the carbon locked up just fine if you make sure to sell it for long term use applications like carpentry.

In theory, hardware like this is designed to function as a solar sink, utilising surplus production during peak hours when storage devices (batteries, dams, etc.) are fully charged.

My question is, wouldn't the power needed to run these negate the benefits they bring?

The hardest part about green energy is getting it to the time and place where it can be most useful. That's why real time solar power prices sometimes dip negative (where the producers are literally paying people to take that excess power off the grid), and sometimes in consistent and predictable ways (e.g., California's "duck curve" in spring and autumn).

So with solar power being the cheapest form of generation, but highly dependent on weather conditions, the solution might be to build up overcapacity where production during cloudy days is enough, and then find some way to store the excess on sunny days for nighttime, and maybe using intermittent power sinks that can productively use energy only when the production is high (charging batteries, preemptively cooling or heating buildings and storing that for later, capturing carbon, performing less time-sensitive computer calculations like data analysis for science, etc.)

If we have systems that produce too much energy, then carbon capture (including through manufacture of fuel or other chemical feedstocks) can vary by time of day to address overcapacity.

What you're missing is they use the carbon to push out more oil from the ground. That's where the profit is.