It's eminently reasonable to have a different goal: prevent the activities whose environmental cost (via CO2) is greater than its economic benefit. In that case, the tax is sufficient to achieve that goal because it adds the cost in directly.

Then, for every case where the economic benefit is small relative to such a cost, people will stop doing it. And even if they don't, the government now has collected an amount of money equal to the environmental costs and can work on mitigating them with it! [1]

(That goal is, incidentally, the point of Pigovian taxes -- or at least, it should be, rather than "to give me cover for restricting something I disliked for other reasons", which is how they often get used.)

[1] If you want to go the route of saying that the costs are unqiantifiable ... don't. That way lies insanity (and arbitrary policy).