Limiting flights would be silly. That's an input, not an output. If we want to limit CO2 (and other greenhouse gasses) then we need a global emissions tax or cap and trade system.
But you know and what you think is silly may be effective and better in the long run. We need more 'silly' ideas in order to find a good one. In contrast, you can't have unlimited flights either, where the toughest and most powerful airline can fly the most just because they can cope with high taxes. That would only favour the big airlines.
We see that this virus has been really effective in lowering emissions. We're talking about changing human behavioural patterns deep within, I don't think taxes can create such a strong force.
What do you mean by trade system? Not sure I understand that.