Depends on the sports, and how close you can get to the sidelines/court/field etc. My 70-200 isn't the greatest for highschool football, but if you get permission to shoot from the sideline it would be great. You could use the 1.4TC though from the stands but you lose a stop and its hard enough to freeze action under crap highschool field lights. It works great for soccer as well if you can sit on the sideline ( although mine isn't a prime and found myself shooting more in the 70-100 range, so I am sure the 200 would work if you backs up a bit from the sidelines. I found it to be too long for highschool volleyball and shot it mostly at 70mm. I think a prime 50mm would be a better range for that. Of course, this is all highschool stuff, when it comes to the pros, you probably want as long a lens as you can afford unless you are rich and have courtside/field side seats. In which case, you can just buy a whole plethera of lenses.
For things like Racing you would probably want to get a longer lens since it would usually always be in daylight anyway and there are much more safety restrictions.