I'm quoting your own quotes, and you must be able to see from these regulations that a CFI must hold an instrument instructor rating to provide instrument instruction towards an IR. Is that what we're talking about?
And in the rest of the post "You review 61.193 and you see privileges. Under 61.195(a)-(c) you see limitations."
The only limitation placed on a CFI is that in order to give instrument flight instruction they must hold a valid instrument instructor rating. Note again it is specific it says flight instruction. Short of this restriction all other privileges are granted.
Again I am not trying to debate what we all assume this should be. I am trying to look for a definitive answer in the FAR's, not speculation.