I agree with your thermodynamics, I'm just concerned about finding a volume big enough to store climatically meaningful amounts of CO2 in that form. 40 billion metric tons per year of CO2 in the form you describe is around 30 billion cubic meters, and you need to find that much storage volume every year just to keep things from getting worse. If you want to actually make a dent, like rolling things back to the year 2000 (which likely isn't enough, but is a real impact), that's more like 600 billion metric tons or 450 billion cubic meters. That's roughly equivalent to 400 mountains 5000 feet tall. It's a huge volume of material we're talking about finding a place to store if we're actually trying to make a real dent in climate change.
If you asked a pre-industrial person how in the world it would be possible to source, refine, and distribute enough crude oil to power the modern world they would quote some similarly breathless numbers. It's possible because there's a motivation to do it. Simple as that. If we had a similar level of motivation to sequester our excess carbon we could start planning to do that tomorrow and have it done within a decade or three. You can't sequester all the worlds carbon in one place, just like you don't pull it all out of the ground in one place. Big problems seem less so when you realize that solutions are usually distributed.
I don't have the sources or exact numbers on hand, but I remember reading that the world's extractive & production processes create something like ~4 billion tons of oil, ~4 billion tons of iron, ~x billion tons of cement, and ~50 billion tons of sand, per year. These industries developed over many years and as you note are distributed globally. With market demand and regulatory pressure, we believe achieving CO2 removal across different modalities at the giga-ton scale is possible in our lifetimes.
That being said, we try to bring a conservative approach to our scaleup plan. The most immediate challenge is demonstrating CO2 removal at the megaton scale (1 million tons per year) to validate the process and meet short-term demand for voluntary offsets.
We also got calculations that yielded literal mountains ranges of carbonate... That's not to say carbonate cannot be part of the solution, but maybe it is unlikely to be the only solution.
