That would be ideal. As I understand it, it has been tried, but without reaching an international consensus, and leads to airlines filling the tanks of their planes in countries that don't tax the fuel, and flying with more fuel than needed (and therefore having to burn more fuel) so they don't need to refuel in countries that do tax the fuel, thus defeating the purpose of the tax.

I don't know if it was widely reported, but in the days before the COP meeting in Glasgow, Britain removed the tax they had on internal flights.