The problem there is that most ways to add carbon pricing are against the self interest of whomever enacts it. Point-of-extraction is especially bad because it places all of the initial burden on the few places that actually extract carbon, who are probably not going to like that idea.

On the other hand, those extractors are operating on licenses issued by governments. So in principle, one could add that do their license, and they would just have to deal with it. A challenge is that the market is global, while licenses are given out by nations. So requires alignment of many nations for it not to be a competitive burden on a few producers.

Taxes are already on the government level, I'm not sure what other hand you're referring to here. Who would a corporation even pay the money to if it isn't enacted by a government?

I guess it depends on the 'who' in those places.

It's not hard to imagine a government rather fancying getting a tax receipt from extraction companies, particularly if it is seen as green. Who would presumably lobby rather hard against it. This suggests the absence of pricing at source is to some extent a result of successful lobbying.

The problem is exports; the government is already making money on extraction companies selling their goods abroad. If they burden them with extra taxes, that'll get translated to the price other nations pay, which will reduce exports, and thus reduce government's profit. In a competitive exports market, a country with environmental taxes will lose to the one without.

Sorry, how does a government bring in tax revenue off of exports? Tarrifs are levied on imports rather than exports.

Sure they would make less money off corporation taxes with lower exports, but as those receipts are generally low anyway the tradeoff going to carbon tax would likely be favourable.

Not directly off exports, but doing any kind of operation in a country involves government getting a cut of the profits via corporate taxes, laborers' income taxes, etc. All of these get smaller if the corporation sells less.

Until every country in the world has agreed upon doing that you still need to estimate CO2 when exporting and importing things from and to the common-carbon-price zone.