Airtravel is also subsidised by the German tax payer. Much more than the 49 EUR ticket. No matter if you are a tourist or not. (Arguably mostly for tourists actually.)
The idea is to push people to use the train, but a train isn't an alternative if it takes 9 hours compared to the 2 hour flight.
And your 2 hour flight easily goes to 4-5 hours if you add the security theatre and the extra overhead that transport to/from the airport entails. They are far outside the city whereas central stations are usually in the city center.