This could be very interesting.

If atmospheric carbon capture is compensated as negative emissions (being paid out of carbon taxes), then this could solve two problems for nuclear power plants.  NPPs are being derided as unable to follow changes in net power demand.  However, if steam was tapped off the turbines to do CO2 stripping, power could be reduced while producing a CO2 stream as feedstock or for sequestration.  This would also allow fast power ramping by closing the steam taps, so those same plants could provide spinning reserve during off-peak hours.

Global Thermostat claims to have the lowest-cost capture technology but doesn't provide specifics from their page.  This looks sketchy.  It wouldn't cost them anything to provide a range of values per kg and it would make their tech much easier to evaluate.

I found a number of 497 kJ/kg for the capture energy requirements, and another one of 172 kJ/kg.  I'm not sure how much to trust these because I have no idea how they are derived or what they include.

A typical modern PWR has about 3400 MW thermal power and an efficiency of about 33%.  Tapping steam at the 100°C level probably reduces that to about 20%, so 100% diversion would reduce output from ~1100 MW(e) to about 680 MW(e).  Available thermal power would be roughly 2700 MW(t).

Assuming 500 kJ/kg CO2 capture energy just for the back of the envelope, and diversion of 60% of turbine steam at 100°C from the low-pressure turbine of a power plant:

Electric output reduced from 1100 MW to 857 MW (about 22%).
Diverted steam thermal power 1632 MW(t).
Potential CO2 capture 3264 kg/sec = 3.26 tons/sec.

Doing this 8 hours a day 340 days a year (gotta refuel sometime) nets you 96 million tons of CO2 per year.  Seems awfully high, but even if the energy cost is 10 times as much, the US's plants could pretty easily pull half a billion tons of CO2 out of the atmosphere every year with off-peak steam.

Now if Global Thermostat would only come clean about their exact energy requirements....

And what do we do with all this CO2?

Shoot it into basalts, maybe?

Storing it underground seems much more dangerous than storing nuclear waste.

Unless it turns into carbonates in just a few years, then it's going nowhere.

Nuclear waste is unlikely to escape and suffocate people.

Great!  But we still have a massive amount of atmospheric CO2 to get rid of to restore the normal balance.  If injecting it into rocks isn't an option, tell me what is.

The two most energy-consuming and expensive steps in CO2 sequestration are:
1) separate the CO2 from very diluted l level in the air, and,
2) Compress the CO2 from atmospheric pressure to thousands of psi for sequestration.
The use of higher-CO2 concentration in power-plant exhaust would make it less expensive than CO2 from the air, but still requires the costly compression step from atmospheric pressure to thousands of psi.

However, the use of almost-pure CO2 from the process of steam reformation of natural gas, coupled with the very high pressures at thousands of psi already existed in the steam-reformation vessels means that:
the use of H2 by end-users, when the H2 is produced from reformation of fossil fuel, would result in by far the easiest and least costly CO2 sequestration.

There are numerous ways to create clean energy, i.e., hydro, solar, wind, wave

Yet the ONLY one that has gone anywhere without subsidies is hydro.  Until you understand WHY, you will never be able to distinguish what may work and what cannot work.

there are countless ways to store the energy cleanly.

No there aren't.  There are maybe 2 ways, pumped hydro and compressed/liquid air.  Everything else demands materials that are toxic, polluting or both.

Why keep using methodologies that create detrimental toxins and then increases the overhead by having to clean them up?

Why, indeed?  Why go after e.g. wind power when it requires many times the concrete and steel, and generates many times the related pollution, of nuclear power?

Nuclear has the virtue that its toxic wastes decay.  They steadily disappear all by themselves.  Give them enough time and they will be gone.

Why not just spend the time and money to develop the known clean methods and devices and not create the toxins?

Because of Green propaganda which induces paranoia about nuclear power, that's why.  This propaganda is the only reason that the industrial nations still burn coal for electricity.  We were on track to get rid of it in the 1960's, but they "saved" most of the world from cleaning up our electric grids.

Show your appreciation by finding the graves of some of these pioneering "Greens" and leaving a six-pack of beer on them, after running it through your kidneys.

It will eventually dissolve into the oceans by itself over decades, or faster with ocean fertilization.

It's going to have to be MUCH faster, because the Arctic is starting to melt some 70 years sooner than projections had it doing.  That can pull the trigger on the "clathrate gun".

Also, it is not clear the present CO2 level is a bad level. Plants like it better than 280 ppm.

Plants got along fine when it was 200 ppm; the Sahara was a forest.  Too much GHG and the Earth turns into Venus Redux.  This is bad, mmmkay?

We need to get things down to a max of 350 ppm and do it fast.