Emissions are approximately proportional to fuel use, so I don't see how a tax on fuel (which would be proportional to fuel use) would have any lesser or greater effect than a credit system on emissions (assuming credits needed are proportional to emissions).
Under the proposal, nobody pays anything if they maintain their current emissions. But if a small airline grows and takes market share from a big one, the small one will have to buy credits and the big one will be able to sell credits. The little guy in effect pays the big guy for taking his market share.
If you tax the fuel directly, everyone gets a cost increase right away which they should pass on to their customers. But it doesn't have adverse effects on the free market like the credit system does. You fly more planes, you'll pay more taxes but in proportion to your new revenue so it doesn't really matter.
(And yes, folks, the environmental damage from any one use is bounded; it can't possibly cost more than the cost to undo that damage. If your model of the environmental damage implies it is infinity, it's just wrong, and it's driving bad policy.)