There are no "right" answers. But I will say that engineering a record and mixing a record are two different skill sets. The notion that if one can engineer a recording well, he/ she can also mix an album well has not proven to be the case, in my experience. It goes without saying that the 2 skill sets certainly inform one another, but they are different beasts. With that said, there are many folks that can wear both hats well.
Also - I get annoyed whenever I hear someone imply that when "they" track a song, by the time they've finished tracking - the song "mixes itself". Perhaps this might be the case in a acoustic jazz, chamber, or other "live" idioms, but a dose of humility and reality are in order. Thoughtful tracking certainly speeds up the mixing process significantly, but let's not underestimate the contribution of talented/ tasteful mix engineer and what he/ she can bring to the table.
-t