Dave, You are right of course.
But, the problem I have run into is where you have odd shapes that perhaps are not symmetrical and the areas don't match.
In particular with a toroid type winding, it is nearly impossible to get the inner winding area to match the outer winding area. If you try to use area current densities it is a nightmare and you can't get the two to sum to zero without a lot of pain and frustration.
So it is much easier to just use point properties and the same number of points to represent real coil winding turns. Then the sum is always zero with no headaches. At least this is what I have found from experience.
Regards, Dave Squires