I've had the 6D2 for a few months now, and I just seem to get better focus out of it using the live view with face tracking, vs single spot thru the viewfinder. Hand holding the camera, no tripod. I don't focus and re-compose using either, I always move the focus point. Is this to be expected? I just get sharper images with the live view. I have tried to check the focus accuracy of the canon 24-105mm F4L IS II lens that I am using with the spydercal, but it does not seem to be off as far as I can tell. I do find it very hard to differeniate the sharpness differences on that scale though.
Coincidentially, I had the same experience this past weekend with my 6D2. I've had mine for 3 yrs. I went Go-Karting with my family and took some pictures of the racing. We were indoors. I had 2 lenses, a 12mm fisheye and a 24~70, both f2.8.
Didn't have any problems with light, but was struggling with tracking. Like you I ended up using LiveView which gave the best results.
I initially had some issues with the camera (seemingly) tracking irregularities in the pavement instead of my subjects. I later realized it was my error (camera setting). I was pretty disappointed with myself for not re-checking my camera. I had let someone take some photos at a family event and they changed some of the settings. Rookie mistake on my part and I've been doing this long enough to know better. One of the 6D2's greatest strengths is its live view AF+Tracking. In action photography, using all 45 AF points can yield extremely good results. I use single point AF when my subject is behind something in the foreground that might confuse the camera. Further these point are cross-type and give exceptional verticle and horizontal focus depending on the lens being used.
The Zone AF (in LiveView) offers the flexibility you mention by allowing you to touch where you want the camera to focus. The joystick on the 5D4 allows easier zone control adjustment via the viewfinder. Its much harder on our camera's using the touchpad and dial, so once again LiveView prevails.
Bay Area - CA
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If you're not using a tripod, then I do not recommend using Spot AF. This goes for any camera.
Like most midrange cameras, the most accurate AF point is the Center AF point. I suggest that you give focus and recompose another look. If you are shooting af f/4, then the difference in focus will be slim to none when you recompose.
An alternative to focus and recompose is to lock focus and track the subject as you recompose. If you enable all AF points and select the Center AF as the starting point for AF tracking in AI Servo mode, then you can focus on the subject using the Center AF point. As you recompose the shot, the AF tracking will stay focused on the subject.
As far as using a focus calibration tool goes, you should doubt yourself just as much as the gear.