Dear Alias,
I did an example object for students - a simple rounded cube.
All the fillets have a same size and G2 continuity. Therefore I will build 8 indentical corners.
As you can see at the images, if I do a corner blend, it will not built a perfect corner but it has some G2 continuity errors. Some of the 8 corners have even different errors.

Because this is the very simple task, when someone is starting to learn modelling, it would be nice to have a tool, which can also produce a perfect corner, without further editing.

If you check the details, you can see, that the Corner Blend tool does a lot of good job there:
- control points are aligned to tangency vector from both sides (D: Quertangente)
- the cuts of the fillets are very clean and aligned to one plane, or blended curve connecting edges.
- default Blending options values are well set
So it would be nice, that also in these basic cases it could build a corner with perfect G2 continuity.
Where could I still type in a different values for base radius and still it would hold the G2.
as you can see on the following photo it is possible with a little bit of editing:
