Ok, this is a bit different from distance field gradient. Your technique is know as "inverse distance weighting" (originally proposed by Donald Shepard in 1968) which also exists in many different flavors, and has been intensively used in many scientific fields for scattered date interpolation (although I don't know a specific application for generation of color gradients.
I do not know, what in particular means "inverse distance weighting", but I do have a solid guess, that my method differs from what are you talking about. Weight of a control point isn't a monotonous function of a distance, moreover, its sign changes.
That's not what I meant. Here is a picture to explain my concern. When computing the gradient color at point P, the influence of the source point S should be weighted according to the geodesic distance (in yellow) rather than the euclidian distance (in orange), because the outline of the leaf should not be crossed. When you use scattered data interpolation, your color blending function is not aware of the existence of this outline, and of course totally ignores it. Consequently, the color of S has too much influence at P, which generates the magenta color bleeding around P. In your example, the result is not too bad, because the difference between the yellow and the orange dstance is not too large, but in other examples (spirals, for instance) it can totally ruin the expected gradient.
You are right, partly, but this prob could be solved in different ways. For example, it is possible to draw an additional line and put some vertices on it. These vertices will impact on two regions.
Again, I don't know the gradient mesh implementation made by Adobe, but gradient mesh should handle such a case quite easily, and should not require many much more seed points as in your example.