The 200 f/2 is the portrait lens. The 135L is the closest thing to it for budget users.
I think you will find that the design brief for the 200 f2 was primarily lowlight and shorter long focal length sports, that it is used very effectively for portraits by some is a complimentary use for it. Certainly if you want to see ten or fifteen 200 f2's together just go to any ATP World Tour event. Canon made the 85 1.2 as a pure no holds barred portrait lens and considered AF of secondary importance to the "look" it gives.
I remember for years the sample images for the 300 f2.8 IS are head shots portraits, though nobody would doubt that portrait shooters are not the primary market for that lens! Though there are a few that use it, for instance I do, but primarily because I have one and don't need the 200 f2.
EDIT: Obviously the 200 f2.8 is the budget version of the 200 f2.
Used the 85L II, Found it kinda meh when I already have the 135L. The 200/2 is the best portrait lens canon makes IMO, its just expensive and heavy. Sure it can be used for sports as well.
The 200/2.8 is a lens I've never been particularly fond of when the 70-200LII does the same thing. I used the 200/2 at a buddys house for about an hour, and instantly knew it was in a league of its own.