Earlier quoted context omitted.
The other alternative is to use the tax income to offset other taxes, or even return it directly to citizens as a dividend.
Then what's the point of the tax? I can see how airlines may funnel some effort into R&D to reduce carbon emissions, but only to the point where it becomes profitable to them. Returning the tax as a dividend to the consumer is just as pointless as the consumer is in no way obligated to be climate conscious with their capital.
If you're wondering "why not use targeted legislative mandates instead of carbon taxes?", I'd say that taxes have an advantage in that they're harder to game and need fewer adjustments over time. For example, if you introduce a mandate to make cars more fuel efficient, manufacturers will tweak the vehicles they sell so they are no longer "cars" but some legislatively distinct class of vehicle, and people who like gas guzzlers will just drive those tweaked vehicles. But if instead there's just a carbon tax on fuel it's a lot harder to game your way around the legislative intent.
[1] Assuming that the balance between just paying the tax and evading the tax still favors paying it. You don't want to impose a $20/pack tax and find that you've just given organized crime a major boost.