There's a yabut in there. Steel...and any other material...isn't 2-dimensional. To say that steel is "stronger material on a per-square-inch-of-metal" basis is misleading. Yes, the strength is given in a pressure measurement but that is more an artifact of the method used to measure the material than any real world property. The strength measurement should also be qualified with a statement about it being a pressure acting on a cross sectional area which you didn't give. Cross sectional area is more closely aligned with a volume measurement than a surface area measurement.

That's how I read your post. When you said that steel is stronger on a "per-square-inch-of-metal", I thought you were describing forces acting on the length of bicycle tubing rather than on a cross section of the tubing. They aren't the same forces. Consider, for example, a pressure vessel. If you need the vessel to hold a higher pressure, increasing the length of the tube does nothing to give you a higher pressure rating. Increasing the length actually does the opposite. Increasing the thickness of the metal, i.e. increasing the cross section, will give you a higher pressure rating.

I do realize that increasing the length of the tubing is increasing the volume of tubing used but the dynamics of the forces are different. In an increased length situation, you've also increased the surface area that the gas is acting on. When the wall thickness is increased, the surface area remains the same while the volume of material used increases which is why I view cross sectional area as being associated with volume.