Can I ask what countries you fly in? I fly frequently within the European Union and I am a EU citizen. However, even for flights between the Netherlands and Germany I have to enter my ID details during check-in and it's checked multiple times throughout the trip.
It's not just random checks, but it seems mandatory. When you drop off the luggage they ask for your ticket + ID. When you board the plane, they again ask for your boarding pass + ID. The exception is large, modern airports such as Munich where you simply scan your boarding pass when boarding the plane.
How do you do this? Do you just refuse?
I have definitely also flown from Germany to Italy and back without ever showing ID. I can also recall flying from Germany to Shiphol without ID, but I can't recall whether I was controlled on the return flight.
It's not 100% ID-free though: AFAIK they are permitted to check ID, and they do it randomly.