Hey, how about 3" x .020 wall? I = .2078, W = .65 lb/ft I/W = .3196

Obviously superior to that wimpy 1.75 x .095. (and 4" x .010 would be even better!)

You need to be careful about the assumptions you are making. There is a lot more to the strength of a cage than the bending strength of the tube. When you go to thinner wall tubing, buckling strength in compression can become an issue, as can the effects of localized deformation. And even in bending, with the same load, the stress on the surface tube goes up with the diameter (or maybe the square of the diameter - it's been a while since I checked). If it's a listed tube, I'm sure they're all ok, but I wouldn't try extrapolating to some thing bigger and thinner without a serious expert evaluating it.