The reason the tube bumper rots is that moisture builds up inside it and then slowly rots it from the inside out. The brackets being flat do not retain the moisture. If you take a look at your factory bumper you will see the end caps are tack welded and not sealded the entire way around which allows the moisture in. Most could prevent the rusting by sealing the end cap and applying a good coat of paint...or be fortunate enough to live in a nice dry desert setting!
As far as round tube not being strong...wrong. Why are tube frames not made with square tube? It depends on the tube material, how it is used and the size/thickness.