This won't work, because when you mix half-transparent pixels with half-transparent pixels, you're getting half transparent pixels: if two pixels have, say, 50% opacity, the resulting merge will be 75% opacity, not 100%.
The only way to avoid this but still get the feather that comes to my mind is to have your blur applied as a post-action: which might be ...
Surely most of us understand well that the effect of a low pass filtering can be neutralized by applying a complementary high pass filtering to a copy of the same image and by adding pixel by pixel the RGB values of the both filtered versions.
To clean someone's portrait image we apply Gaussian Blur to the image as a special form of low pass filtering and ...
Recent versions of GIMP have non-destructive erasing, to allow use of the anti erase function of the eraser tool. The eraser in GIMP basically edits the alpha channel without erasing the pixel data itself, but software such as MS Paint totally ignores the alpha channel when copying and pasting directly from GIMP.
To permanently delete the erased pixel data,...
This is ok if you can accept limited number of colors like in indexed mode. If you convert you image to indexed mode you can have only one kind of transparency which hasn't a slightest hint of the original color.
Gimp likely is not aware of the capabilities of the receiving end of the copy/paste so it copies what it has.
Easy work around:
Add a layer below your image
Fill with the default background you need
Another method could be to use strokes with *profiles** assigned and a Blend.
Simply create a blend between a few paths with stroke profiles. You can then duplicate the blend object and move the paths around to create different variations.
I am pretty sure there are many ways one could go about this. One method is to use narrow ellipses filled with a gradient. These are all the same ellipse copied and pasted multiple times, some narrower and some wider, and some I edited by moving the red stop so it comes further up the ellipse. Everything is then cropped by using a clipping mask over a black ...