> it should be exactly equal to the cost of carbon offset for the amount emitted

If it's to fix an externality, then it specifically should be exactly equal to the cost of that externality - that is, sufficient to compensate for all damages (and repairs for said damages) resulting from that externality. This should be right around the same as a carbon offset, but it's worth remembering why a carbon tax is necessary: not for the mere sake of punishing some dirty activity, but for the specific sake of compensating the victims of reckless negligence.