I flew with Air Berlin a few years ago. Their bike policy then was the same: just roll it on.
Otherwise, Lufthansa have very steep bike charges ime

British Airways is my go-to

afaik baggage handlers are employed by the airport, not specific airlines... thus if you have a change of airport, I would be vary wary of them loading my unprotected bike :/

I'd read and re-read the bike policy and go for the cardboard box if it's the same charge