That pic shows why on flat sites, I just add catch basins periodically along the path and grade long swales to get water to them without crossing the path.
On gentle slopes, its usually easy enough to fit the path in, but where its flat, these problems creep up far too often not to take care of it in the original design. More basins, oh yeah!
Even with the best grading, it seems that silt and or root mass builds up along these paths, and causes even more problems. I try to get the finish grade on the low side of paths down an inch to allow for some of that. However, if you go too low, carts slip off the edge, create ruts, and make even a worse problem.