Anti-aliasing or dissolving pastes into a background.

This is a question and discussion of the existing ways, and a proposed way, to blend or anti-alias a pasted object.

Suppose you loosely select an airplane from a uniform sky background, copy it, and paste it somewhere else. If the background was not very uniform, the paste might have jaggies (aliasing?) or a noticeable disconformity where the selection line was.

Magic wand could be used to do a better selection.
Or you could smudge (blur?) the disconformity.
Or you could use the select foreground object tool.
But each of those might have problems ( especially if the background has much irregular texture, or if there are shadows, or hairs, etc.)

Are there any other ways?

I was contemplating a script that uses the resynthesizer. The script would resynthesize a band on both sides of the selection line, in effect dissolving any differences between the background of the copy and the background around the paste. Thats my proposal. I think it could still leave a halo in many cases.

And whats the right word for this operation? I would have said blend, but that seems to have another meaning for most people. Is dissolve any better? Smudge/blue is not right because it implies a loss of resolution?

most simple is shrink

most simple is

shrink selection of few pixel
invert selection
apply gaussian blur
(more the radius more the feathering )

invert again selection and clear

This work if the layer is on top in normal mode, partially selected pixels may have weird effects if the layer is in other modes