Flying from Berlin to Brussels without showing any ID

It was really surprising to see that there was absolutely zero control of any ID on the flight between Berlin and Brussels. I'm well aware of the marvels (and data protection nightmares) associated with the Schengen agreement. However, zero form of identification on air travel was really a big surprise to me. Not even my flights inside Germany had this 'feature'

How did this work? First of all, I booked the tickets through a travel agent quite some time in advance. No form of ID required (though he has my banking details). Next, I did a Lufthansa online check-in from my home, printed the boarding pass. On the airport, used the self-service luggage drop-off counter. Then directly went to the security check, and then to the gate. During the entire time, nobody asked for any form of ID.

So if I did buy the tickets on cash rather than with bank transfer, it would actually still be possible to travel under false name and thus anynomously. Amazing. Am I missing something?