Nice to see not many people recommending lenses less than 85mm. After talking with several professional photographers, I have recently learned that none of them recommend shorter focal lengths due to distortion of the subject. They all like to see 85, or even 100 or more for portraits. At least for FF cameras. They joke about people who shoot portraits with 50mm or less focal length. Maybe it's time to trade in my Sigma 30mm/1.4 for something longer. I suppose for my 70D, I might be able to get away with a 50mm since that would be 80mm FF equivalent.
It depends on what the OP means by 'portraits', but if you mean posed, formal portraits then you are correct. In such cases it is best to keep yourself at least 12 feet back from the subject, which will require the use of a longer focal length to frame the shot.
But if you take a broader view looking at environmental portraits or other 'people' photography, there is no reason to believe that wide angles cannot be used. You can find specific examples of what I mean in this thread about using a 24mm prime on a FF camera here:
Specifically, the OP has a 70-200 zoom that he's perfectly happy with. He seems to be looking for a better lens to replace or use instead of his 24-70. I'm not sure how an 85mm or 100mm prime solves the OP's stated goals in any way.