Yeah, but the main point of an exo cage is to bash along obstacles without damaging the body. I can say with the way my truck is back-halved, it is very nice to know I can rub on rocks or trees and cause no damage.
I don't see the bending moment of 1", especially 0.060" wall (even in chrome-moly DOM) taking the punishment. Plus, the thin wall will be succeptable to denting.
And, of course, 1" tube for an exo would be asthetically disgusting.
The 1.5 - 1.75" size is generally the nicest looking from that standpoint.
What you make it out of is up to you, and depends on what your local steel yard carries.
I buy from Pontiac Steel, a 21' stick of 1-1/4" sch 40 A500b is about $35, when I bought last. Often, the HREW (hot rolled electrically welded) tubing you buy is also the same A500b grade, so don't be afraid of the word 'pipe' (read my 'poop pipe' thread for more info in this forum).
For reference, your weights would be:
1.5" x 0.120 wall = 1.77 lbs / ft
1-1/4" sch 40 (1.66 x 0.140wall) = 2.27 lbs / ft
1.75" x 0.120" wall = 2.09 lbs / ft
BTW, what type of bender/dies do you have? That kinda makes the design..