I was actually thinking about it for years but only now I made an effort to illustrate it and post is somewhere...
For me it seems this would be really helpful for designers, especially for creating advanced, non-uniform shadows (for example a very common effect is a sheet of paper with one edge bent upwards - the shadow cast by such non-flat object will not be 'flat' but more blurred under the bent edge).
Another example is masking and object with dept of field, where part of the image is sharp while another is out of focus. With interpolated feather you could draw a vector clipping path an apply different amount of feather to a part of the path depending on how sharp/blurred the image is.
A quick illustration:
It would probably make sense to also modify the interpolation method or 'easing' between to points with different feather amount.