I just
cut rectangular holes in rectangular tubes for smaller tubes to pass through and will say in my case of passing smaller 5/16" wall tubes through larger 5/16" tubes there's more resulting strength than butt-welding, and I would think that in the case of the front-end loader if a smaller round tube was passing through the larger loader arm rectangular tube the strength and rigidity would be increased. Mind you I'm not a tractor or loader engineer, so it's only a guess.
From looking at the initial pictures it looks like poor heat penetration on the loader arm side of the weld (a "cold weld") resulted in a stress fracture. Welding is supposed to be using an arc to heat both parts (the loader arm and cross-tube) to the point they melt and steel from each flows together into a pool that when cool forms one continuous part. The filler wire is to make up for the loss in material that vaporizes due to the electrical arc--it's not glue and doesn't add strength when used as glue; in fact too much weld reduces strength (it's a bit more than worth detailing here, all that is in the AWS book).
I say "looks like a 'cold weld'" because from the pictures it looks like the filler sits on top the cross-tube and loader arm instead of the cross-tube and loader arm being slightly melted away and into the filler; any time I see a "caterpillar" type weld that's
usually the case, the filler is forming a convex (bulging out) round ridge mostly on top the donar parts with little burn-in. A weld with good burn-in generally shows material contribution from the parts being welded and is concave (bowed in) or flat across with smooth (not sharp) transitions between the parts and filler. (As a note, sharp transitions usually result in high concentrations of stress at the sharp transition. In this case smooth transitions are a function of sufficient heat to make a good weld and also benefit the weld by not creating a localized high-stress point.)
Also note we MIG weld low-carbon steel plate (and tube, angle, bar, etc) daily and there's no problem with burning through the scale and creating a strong weld, I've posted quite a few photos of heavy welds we've done and burning through mill scale isn't an issue.
Looking at the repair I see a multi-pass weld that looks "pretty good." I don't see porosity, there are a small amount of slight voids but it's not a shielding gass issue. To me it looks like the welder pulled the weld (instead of pushing it) and the welder likely kept a good puddle and constant heat, so all good there. BUT, look at the weld distribution. I'd guess it was welded out of position and there was not enough heat--lots of motion on the part of the welder caused a good looking weld though not a strong weld--it looks like there wasn't enough penetration for good penetration as evidenced by the lack of burn-in. (See how on the left there's a small smooth radius between the filler and the tube, and in some areas the filler sits on top the tube? And on the loader arm there's a sharp transition between the filler and the loader arm? To me, from one picture, I would *guess* there's not much heat penetration. Looking at the steel and looking at the paint, I'm not seeing evidence of melting the cross-tube and loader arm together, rather it looks like the opposite happened with both being unscathed.)
I say this hoping to be helpful, not criticize anyone's work. When I saw the repair I cringed and likely left an :O or

face out of concern for the result, which it seems showed up much sooner than I'd expected.
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If you look up the word "weld" with the gear icon and enter WI_Hedgehog (or leave me out, whichever) there are other threads on welding that might help. I do have a few pictures in the
D-ring thread, though that also doesn't make me an expert--in fact I should be the first to tell you there's a lot more involved than what has been talked about here as certified welders will tell you. And as has been
mentioned by McMXi, a picture can only provide some of the information, which is why I say "guess" and "looks like" a bunch, plus I don't have the experience an instructor or certified inspector has, so it's a guess based on experience, but still a guess.