If you are talking about a welded steel-tube truss structure, square tubing has indeed been used successfully. As you mention, the joints are often easier to fit because the cuts are straight. And, it would not necessarily be any heavier. Here's why:
A truss structure gets its strength from forming triangles. One of the unique properties of a properly-designed truss is that, when it is loaded in bending (in any direction) or torsion (in either direction), each of the individual pieces of tubing is loaded either in pure tension or pure compression. That is, there are no bending or torsional forces on any of the truss members. That is why a truss can be made very light using thin-wall tubing, but still be very strong and very stiff.
So, from an engineering standpoint, what does it take for each of the tubing members to withstand the tension and compression forces. Well, first, an engineering analysis would need to be done to establish the magnitude of those forces under the design loading conditions. For the tension loading condition, it is then a simple matter to calculate the strength of a particular size of tubing based on its cross-sectional area and the tensile strength of the steel.
However, the compression loading condition more often determines the tubing size required. The ability of a piece of thin-wall tubing to withstand compression loads relates to how prone it is to buckling, rather than pure strength. So, what controls buckling?--answer: the unsupported length of the tubing between tube clusters and the cross sectional shape of the tubing. Obviously, the longer the unsupported length, the more prone it would be to buckling (that's why wing struts often have a "jury strut" about halfway out--to stabilize the strut under negative-g loads. For example, a long unsupported length under a given compression load would require a larger diameter round tube to support the load without buckling.
From an engineering standpoint, a better way to say it would be this: the longer the unsupported length under a given compression load, the greater the cross-sectional "moment of inertia" or "radius of gyration" would need to be. These are arcane engineering terms, but suffice it to say that a 1" x 1" x .035" wall square tube has a higher moment of inertia than a 1" diameter x .035" wall round tube. So, if the unsupported length and the compression load required a higher moment of inertia or radius of gyration, I might be able to use a square tube instead of a round tube of the same dimensions. Yes, the square tube will weigh more per foot than the round tube. However, a proper engineering design would involve trading off the required buckling strength against the weight and it might turn out to be more advantageous to use square tubing.
Some years ago, I designed a welded-steel-tube truss fuselage for an ultralight, where minimum weight was absolutely paramount. It turned out to be more advantageous to use square tube for the members of the truss primarily subjected to compression loading (upper longerons) and smaller round tube for members primarily subject to tension loads (lower longerons) and short cross members.
Of course, engineering design is always a compromise between not only strength and weight, but also cost, ease of fabrication, serviceability, and other factors. It is easily possible to design a light aircraft that will handle all its required operational loads just fine, but be so fragile that it cannot be easily moved in and out of the hangar without damage!
G. Michael Huffman
SportAviationSpecialties dot com