It never occurred to me that staying under 50# for bike and box might be a problem. I have never used anything heavier than a cardboard box, but have taken a fairly heavy steel framed bike with front and rear racks and never exceeded 50#. I guess those more robust cases are heavier than I realized. A 22# box seems pretty heavy and a lot of touring bikes would indeed take that over 50#.
I forget what it weighed so I may be off a bit, but I don't think my soft case was much over 4 pounds. It is pretty flimsy though, but a little cardboard and some clothing and gear (that I need to take anyway) for padding and the bike is pretty well protected. It takes some pretty careful gear selection and packing to keep total load under 50#, but with some in a little personal item sized backpack it is easier. With a carry on sized bag it is very easy, but then becomes harder to carry it all at once.