I think you want to reduce the surface runoff of mud, going down a hillside.
But you're looking for plants with a single stem, and as wide as possible!
I'm just typing as I think, but wouldn't you need continuous roots near the surface to hold on to the SURFACE soil? Like sod (a mass of tangled roots and single stalks)? I would be thinking of cover crops like clover or alfalfa or something tolerant of drought, heat, and steep slopes.
My mental image for single-stem wide plants is one rootball every (say) 12 inches.
Wouldn't the surface soil just wash away from between each plant, except for a few square inches right around the stem?
Maybe plant roots reach for the surface more than I think. But I always assume I can cultivate an inch or two deep all around my vegetables, and even close to the stems, I expect to see no roots for the first inch or so.
If a whole inch washed off a hillside, it might fill your pool to the rim!
This is just speculation, so ignore it if fairly widely separated bushes can work for erosion control.
