With potentially the entire "adult" population of a state involved, an artificial restriction and rationing/trading system it would be, too put it mildly, a hideously difficult and expensive system to put in place. To say nothing of the "fun" of trying to roll it out globally. It's an over complicated point solution and it could only make sense if it's believed that air travel is a fundamental human right, alongside being fed, not being routinely tortured and that sort of thing.
The best idea instead is to simply let market forces decide but tax it properly. Fly, but pay a fair share for the increased health care costs, double glazing, property devaluation of all on the flight path. Fly, but pay a proper share towards the global cost of the CO2 emissions, towards the lost land and sea productivity, animal extinctions and sea defence costs.
What we do need though, be it for air travel, guns, autos, plastic, whatever; is to become massively more agile at taxing the service providers and producers according to the costs inflicted on our society. The Romans' knew Lead was poisonous, yet Lead was allowed in our plumbing, gas/petrol and paint right up to the twentieth century. Similar legislative torpidity in the face of scientific evidence and fairness applied or applies to tobacco, guns, alcohol, cars, drugs etc. How? It is not getting the right result that is the problem. It is getting the evidence acted on quickly enough before significant problems occur. Because unlike with Lead, we do not have thousands of years for our Politicians to get it right on Climate Change.