If you could offset the carbon emissions for 10 EUR, maybe add 12 EUR to the price of a ticket and use that money to buy carbon offsets? That way those who still want it can still fly, and we're at net negative emissions.
Economics is a powerful tool.
There's no apples to apples price comparisons that can be easily made, where say car vs plane is say 30 vs 42 euro, and this 12 euro tax clearly doubles the price difference. Car trips are typically priced as a per-trip cost that only counts fuel and sometimes parking, whereas air tickets essentially include everything from airport to airport.
But what's left out for the car trip is the cost of ownership (depreciation/maintenance), taxes, insurance. It can't be compared to a flight ticket very easily for most people unless they make a quick Excel sheet and plug in some numbers. And even if you include all those other costs of ownership, how much can be attributed to that single trip by car to replace that flight, if the car is used for other trips, too?
The same calculus goes for time as it does for price. An airport to airport travel time cannot be directly compared to a door-to-door car trip. You'd have to include trips from and to the airports as well as the boarding/security/checkin stuff, as well as a safety buffer not needed for car trips.
Not to mention the experience differences, which are difficult to value. Should a plane ticket be compared to a taxi, because it includes the price of the chauffeur in both cases? Obviously not, yet we also can't just ignore the cost of having to drive concentrated for hours yourself versus sitting in a plane.
In short, while raising the price by 12 euro tax of course does have an impact, but it may not get the impact an economist or policy-maker would expect. It may just go into a very muddy calculated comparison between car/plane (or otherwise).
Second, the tax shouldn't even be such a granular thing. Domestic flights have far greater greenhouse gas emissions than bus, train or car travel. If air was say 30% more poluting than a train, then nudges with taxes would help. But if it's the equivalent of 250gr of Co2 per km travelled [0], and the Eurostar train is 6gr and coach is 27gr then banning seems to be the quickest solution. There's good reasons to say that if mobility option A pollutes 40x more than option B, that you ban A instead of trying to nudge consumption via taxes.
The last thing we need is the insights of an economist when it comes to solutions to climate change. It's thanks to economists that we're still dealing with the problem in the first place!
But it also helped prevent large scale wars which may have emitted loads of CO2.