The bottom line is:
This is theoretically impossible
If you think about it, object, generated, mirror (and any other auto-generated texture coordinates) can be as detailed as is necessary -- they are not based on the detail of the mesh. UV maps, on the other hand, are very much related to the detail/design of the mesh object. This is often called comparing apples and oranges :)
That being said, the only way to fake it would be to use a texture (to get much more detail than a mesh, but less than auto-generated coords) as mentioned here. If it would be easy to convert the clean object or generated coordinates into uv-maps, game devs would be using it everyday...but there isn't. So for right now we just need to stick to smart unwrap and our uv seams ; )
Finally, if you're still not convinced, take a look at this mess of auto-generated coordinates...
Here I am mixing three different texture coordinates (generated, window, and reflection) and using the result in the checker texture's vector input. This material is applied to a cube and however you manipulate the uvs, you will never be able to mimic this mapping because these texture coordinates act like textures themselves: the massive amount of warping from the checker texture is only because of the strange texture coordinates. Oh, and about the texture coordinates acting like textures themselves...have you ever tried to apply a texture as the model (I mean a diffuse/albedo/color texture not a displacement map)?
Yet another reason as to why this would not be feasible or even desirable is that the texture coordinates, excluding uvs, are all volumetric while the uvs are two-dimensional. Therefore, as soon as you "converted" to uvs you would have lost the most important benefit that the object texture coordinate gives you: flexibility.
I hope this helps to clear up your question effectively.