Rectangular or triangular cardboard boxes offer little or no bend and crush resistance. Shaking a cardboard bow box is not what UPS, FedEx, USPS, etc., will do - they'll drop it from a height of 6' - 8' onto concrete and then throw a stacked row of computer monitors on top of it. You are taking a far greater chance of bow damage with such flimsy shipping vessels.
Stout tubes are THE way to go for the best compromise of cost and protection. YES, it costs more to ship with PVC tubes. It all depends on how much you care about the bow being shipped, what intrinsic value it commands, and if it's worth protecting for both the seller and buyer.
Chances are, your cardboard boxed bow will ship without serious incident ... but then again, as I said before, good luck .......
Oh yeah, shipping vendors don't wanna part with THEIR money when a bow gets a smashed limb ... and trust me, they WILL make an issue of the vehicle you used to ship out the bow when you put in for your full insurance claim. Words to wise.