The money equivalency is the problem, not sure taxing it will work either, only because will set the tax too low, or it will get raised too high and be used to do something unrelated. It doesn't matter if they pay enough to sequester equivalent carbon, it matters if it actually gets done. What if we tax, but in the form of stable or usable carbon? If you emit X tons of co2 then you have to bring Y tons of coal, diesel, crude, diamonds, graphite, preserved wood or whatever, to government sequestration sites, or pay someone else to do so. Laws to prevent the government from using the stuff, and you'd drive up the price of fossil fuels simultaneously to account for their externality as well.
> or it will get raised too high and be used to do something unrelated
That matters very little. Carbon taxation is a Pigovian tax, and just making emitting CO2 more expensive creates strong incentives to stop emitting CO2. It also makes "green" alternatives comparatively cheaper.
In fact, many proponents of carbon taxation support equal redistribution of the tax money to everyone (e.g. as tax credits). Taxpayers polluting less than average would see their tax burden decrease, while those polluting more than average would be paying more and thus be incentivized to change their behavior.
(Of course, it's not that easy in the real world, some behavior can be extremely hard to change without help/subventions/large investments. But these helps don't have to be tied to carbon taxation.)
Well that would drive up demand for fossil fuels and profits for extraction companies, leading to more extraction. Is this a real idea (proposed policy in a country) or just something you wrote down?