That's not how it would work. If an airline company plans to emit X amount of CO2, they need to buy the right to do so. The cost would only be indirectly paid by consumers through the cost of their ticket. You can think of it like a currency that polluters need to spend (or more accurately, eliminate, since there is no recipient) when they pollute.

Capping and trading is the more simple solution. Instead of putting various restrictions and limits on a ad hoc basis (often influenced by lobbyists and special interest groups) for dozens and dozens of activities, you have just one unified system.