The current Blur brush is difficult to use in cases where the mesh topology is not very uniform. More vertex-dense areas will get affected by the weight blurring "less".
Here is a simple example:
As you can see, when the cylinder has fairly uniform density, the result I get from blurring is what I expect(even if it looks ugly in this example), but when I add extra edge loops, the result is totally different. This is not necessarily unexpected, and in some cases it might even be desired. So here's a more realistic example, on an actual character with details modeled in:
Notice especially the banding of the colors. I was blurring it as much as I could, but there'd still be clearly visible bands where the topology is more dense.
If I remove some edge loops to try to get more evenly distributed faces, I can make a clean gradient again, with no bands:
The goal would be to be able to create a clean gradient like this, even with uneven topology. This could allow rigging more complex meshes "directly" rather than using indirect methods like Mesh Deform/Surface Deform, which come with their own sets of inherent limitations.