Short answer, no, I don't think a mule would be a great blade for your described task.
Long answer....
Long time lurker, recently signed up, and here with my first post and some experience that might be of use to you. I weed my yard with a knife, and I have cycled through multiple knife manufacturers, steels (including 420hc, 12c27, 3v, cruwear, 20cv), and blade/edge geometries (recurve, drop point, clip point, wharncliff, in hollow/flat/sabre grinds) trying to find one that works pretty well in what is an overtly abusive environment. I too have sandy, rocky soil, and while I don't have goat weed, I do have bull thistle, clover, and dandelions, oh my!
In my experience, a plain edge dulls quickly and makes weeding frustrating. Even high hardness/high carbide steels are brutalized by repeated thrusting through sandy dirt. This is like an CATRA test, only with sandy dandelions instead of silica impregnated cardstock. The cruwear PM2 in this pic did pretty well (you can see what my soil does to the DLC), but it would still be super blunt (as in can't cut a dandelion root) by the end of an hour plucking dandelions. Cruwear is obviously a different material from those currently available in mules, but the PM2 blade shape and size are similar. I don't have a mule for comparison, though once the K294 mule is released I'll fix that
. If you want/have to do a plain edge, I think the wharncliff profile did the best to preserve/protect the cutting edge, since the cutting edge encounters less of the abrasive material while entering the ground. You should still be prepared to sharpen after every weeding session.
The knife I am on now is the Byrd Cara Cara Rescue 2 in 8Cr13MoV. It has a 4" serrated edge, long enough to reach under most plants, and with a thick enough spine and tough enough steel to permit some torquing without me worrying about fracture or chipping. I ended up modifying the tip a bit with a regular hardware store bastard file, though even the unmodified blunt end got into my dirt without too much effort - you can see before and after in the pics below. My initial impression, based on a about a week of use thus far, is that the serrated edge holds its cutting power better than expected, and far better than I was expecting for the 8Cr steel in this environment. I suspect that the leading edge of the serration protects the trailing edge and valley from some of the abrasive wear, and I am then using this protected edge to cut.
I have sharpened it a couple-three times this week, as much to get a sense for sharpening serrations as out of need. When sharp, it shaves hair and easily cuts paper. While it does neither of those after a few minutes in the yard, I am still getting the roots cut and the weeds out. Of all the knives I tried, this one has the greatest promise so far under these circumstances. It will be interesting to see how the serrations and my opinion hold up over the summer.
I hope this helps - let me know if you have other questions or need clarification on this, my newest short story, Knife Choices for Weeding in Awful Soil.