An interesting technology to help fight climate change

IIve read a few articles on this Canadian company pulling CO2 from the atmosphere and using it to create gasoline, Avgas and diesel.
https://en.m.wikipedia.org/wiki/Carbon_Engineering
https://carbonengineering.com/about-a2f/
Im thinking if this was powered by a ARC reactor such as:
https://www.reliableplant.com/Read/2703 ... ctor-waste
We could kill 2 birds with one stone environmentally, using up and reducing the amount of old nuclear waste we've generated over the last 60 years to power the process to pull CO2 from the atmosphere to create fuels that then don't add any additional CO2 to the atmosphere when burned (because all their emissions were already taken from there) and use that to power the airplanes, trains and ships that in is not feasible to electrify.
As there's a lot of smart well educated people on here I'm interested in your thoughts, or am I missing something basic (besides peoples knee jerk anti nuclear bias) that makes this a dumb idea? I couldn't find any info on the actual amount of fuel they can create per tonne of CO2 they pull from atmosphere, but they have a pilot project in BC, and an article I read a little while ago said they were partnering with some oil and gas companies in Texas for another plant The nuclear thing is my idea to make it a process that tackles 2 problems at once

Interesting article. It does use the correct carbon cycle, just recycling the carbon currently in the environment, much as the biofuel production of ethanol does.
In our state and country we have another similar idea, cracking water to get hydrogen, then locking it into ammonia for transport and storage. You then crack it out before use in fuel cells.
Cost effectiveness is the key. As fish stocks have dwindled, it has become cost effective to farm salmon, rather than to go fishing. As yet to me this appears to be a more complex system than just refining crude oil.

It would be much simpler, easier and cost effective to build Ocean Thermal Energy Conversion systems to generate energy. The energy can then be used to create hydrogen fuel, smelt Aluminum or other energy intensive industrial processes. The byproducts are massive quantities of desalinated fresh water and plankton blooms that extract massive quantities of CO2 from the ocean and atmosphere.