I have a 5DIII, 85L II and a fast moving 2-year old. I bought a 70-200 2.8 II as I was finding the 85L too slow for a fast moving kid outdoors.
Indoors without flash you are limited. I get an extremely low keeper rate between 1.2 and 1.8 with the 85L - the DOF is just too shallow if my kid is moving. The pics are 'OK' but keeping the eye in sharp focus is almost impossible. At higher apertures things are better but it is still a challenge - you need AI-SERVO and good tracking skills. But when you get one....
I tend to chase at a higher aperture and then if he sits still I can rapidly dial it down to get that narrow DOF look if I want it. The comment that the slow focus from near to infinity actually comes into play when chasing a moving kid - they come close, then run away. You miss a lot of shots due to that.
In summary - it works, sort of. Does it work $2000 worth? Probably not. Learning better flash skills may pay off more.
85L is not a lens that is meant to be on the camera 100% of the time. It's for one of those movements when the son/daughter is working on a puzzle with the mother and they are "in the moment" and you go in and do your thing and get a dreamy picture. That's at least how I am planning on using it. If you are "chasing" anyone with this lens, you are using it incorrectly. You need a 35L/24-70 type of lens for that (which I own - 35L). This is like taking a Porsche Cayenne to a race track and racing against a BMW M3 or doing the opposite, taking the M3 and trying to drive in country roads that's covered in snow. I think for your "missed" shots, you need a 35L. All those shots you mention are meant for a 35L, I speak from experience.


