If it is a pavement slab rather than a building slab, no thickening would be required, as with the curb there, you obviously don't expect traffic transverse to the edge. But as the slab is shown as 4", and the grade is lower than the normal slab soffit, there will have to be some thickening to make it work. And as you indicated, erosion must be considered.
A thickened edge actually promotes shrinkage cracking of the slab, as the thickened part shrinks slower and less.