the vertical walls of the connectors add strength, and there is not much to gain going wider than the front and rear subframes [which are around 2" wide]
although i have never done this comparison, it would be interesting to compare a piece of 2x3x1/8 thick [or 12ga-.105 thick] to a piece of 2x2x 3/16 or 1/4 thick.
not much difference in weight [we are looking at commonly available material], but what would be the torsional differences ?
just a reoccurring thought.