Letting european airlines pay for "domestic" intra-european flights where all other airlines flying into the EU do not have to pay is a direct threat to all european based airlines that do compete on an international level.
I don't see any logic here. Intra-European flights do not compete AT ALL with Europe-Asia or Europe-US flights, so the pricing structures are completely independent. An airline only needs to increase the price of those "local" tickets to cover the carbon tax and the brokers' profits & commissions.