My brother and i recently went from Edinburgh to Bordeaux with RyanAir. I don't find it's the airlines fault but the airport / luggage handlers that have the issue.
I use a plastic bag and it was fine, it's easier for the luggage handlers to carry. When i got to Bordeaux my rear derailleur hanger was bent. I was able to straighten it by hand, but i was a bit p!ssed. On the way back the Bordeaux airport people had problems getting the bikes through the x-ray machine and wanted me to lower my seat. I tried to explain, in my best french, that my tools were in my bag that had already been checked in and with a little help it went through ok but it was a major hassle. Anyway i didn't think we'd see those bikes again and i was shocked to see them unloading the bikes in edinburgh. Our bikes aren't very expensive, which was good as i saw the Edinburgh luggage handlers not really treating the bikes (or any luggage) with any sort of care.
A cardboard box may give you a little bit more cushioning, but the next time i take any bike on a plane i will fit a rear derailleur protector.