The shipper was lucky. Even if the cue was insured, the claim would have been denied. USPS requires "fragile" items to be double boxed, and will not pay off in the event your item is damaged unless it was packed according to those guidelines.
The triangle tube is fine if another tube is used inside. U-Line sells 3" .125 cardboard tubes that are 36" long. Those tubes are stronger than the white .088 tubes USPS and others sell. The same cue, packaged inside a tube as well as the triangle box might have not kept it from damage, but would have kept it eligible for an Insurance claim.
I never ship a cue in just the round tube either, they have a tendency to roll around and wind up lost or in places more susceptible to damage.
I have used PVC pipe inside a triangle tube too, but I believe the thicker cardboard tubes work well enough.
You can also see from the damage that shipping Express makes no difference in how safely your package is handled.
Hell any Home Depot or Lowes will give you carpet tubes. Won't be anything breaking one of those...
(Like measureman said...(just saw that))
JV