Thats why there is a need for a global Carbon Tax/Pricing System. This would internalise the cost of pollution and make engineering solution more important from a market perspective.
Why not simply make it illegal to exploit fossil fuels? The result is the same, except that making it illegal has a certain result, as opposed to a tax that is less direct. Of course it's very hard to make it illegal, but I don't think it's easier to enforce a carbon tax that actually works.
Making things illegal is prone to micromanagement. If there are ten thousand industries dependent on CO2 emissions how are you going to pick the non essential ones and only ban the ones that are truly bad for the environment? What's the likely hood that officials will simply misjudge a specific industry? (maybe even on purpose?)
The reasoning behind the carbon tax is simply that every participant can make a decision for themselves. "Do I need CO2 emissions to run my business?" "Does a different business have a greater need to emit CO2 emissions?" This is the type of thinking one is trying to encourage with the introduction of a CO2 tax.
Making things illegal is roughly equivalent to putting a very high price on them. A steadily increasing carbon tax is the economically feasible way of stopping extraction.