> All extracted carbon will be eventually burned.

Extraction operates on supply and demand. When people stop demanding it, they'll stop digging it out of the ground.

There are two ways to achieve this: 1) You make burning it more expensive (carbon tax). 2) You make alternatives to burning it cheaper.

You can do both at once. In fact you want to, because the first one gives the second one economies of scale and the second one reduces the economic impact of the first one.

Preventing extraction is pointless because it has the same effect as the first one except that instead of the money being collected as a tax that could be refunded to the population as a tax credit, it goes to the people who are still doing the remaining extraction. We could, however, stop subsidizing extraction.