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.