I've had tags cut off by QF baggage handlers when they decided it was "inappropriate" -- including Star and Skyteam priority tags! For example my DL PM/MM tag which is laminated and good for many years was neatly cut off with scissors. I filed a claim with QF for damage to my bag (same as cutting off the name tag) and they paid up (I was flying F and they decided paying was cheaper than the hassle of getting DL to reissue my missing tag). Not sure why QF does this (nor has any other airline done it, at least not with a neat scissor cut).

One last point: at many airports, the priority tags are just eye candy for the pax; the actual priority is encoded in the bar code and used by the automated sorting machines, so it matters not one bit if you have F, J, priority or no tags -- the bag is sorted/loaded based on the barcode which has more than just the destination info. Probably CNS/CBR isn't like that though.