Do you think oil extraction companies and countries should pay the Carbon Tax?

Oil companies and producer countries are selling us oil products and making huge profits. But then only some of us have to pay carbon taxes on the products we buy (directly or indirectly) because their products pollute the world with CO2 emmissions. Do you think it would be simpler and fairer for oil companies and producer countries to pay a carbon tax at source for every barrel of oil taken out of the ground? Polluter pays, the world has the money for mitigation, and there is a level playing field for all consumers across the world.