I think I must be doing something wrong. I'd quite like to know what. Until then, I will stick with AF-S because it is reliable and trustworthy.
There is no reason whatsoever to use AFC for static subjects. None.
Agree. No reason to use AFC for static subjects. AF-S could maybe even be more accurate (smaller focussing box also), but so far I didn’t encounter any problems (accuracy and speed). when using AF-C. So, you could also say, that there’s no reason (at least for me) to use AF-S instead of AF-C.
In fact, manual focus (with magnification and/or peaking) might be even better...
Sorry to budget in here: I have started using AF-C with my A7RV 2 years ago. Doesn't make a dime of a difference either way, static or moving. Everything, we'll, not everything-everything but mostly 100% is in focus. All the time.
Deed
But are we talking about the same thing?
In AF-C mode with my A7Riv, if I point the centre focus point at say a book on my bookshelf and half press the shutter release, then move the framing to something a bit closer, it refocuses. If I then move it to a different object on the shelf it refocuses again, even if I move it just a fraction.
This is the expected behaviour with AF-C and I imagine exactly what you experience. The camera constantly refocuses in real time on whatever is under the centre point as long as I hold the half press.
It makes sense it does this for moving subjects. But for static subjects, once I have focused the camera, I want to be free to move the framing around until I have the composition I want without the camera refocusing: I have already chosen my focus point, I don't want the camera changing this. AF-C is really disconcerting for static subjects because it keeps focuses on whatever is under the focus point, and not what I want it to focus on.
I suspect the camera can be switched to some other mode where it will continue to hold the focus on and track the book I first focused on as I adjust framing, but I don't understand the AF system and what the settings need to be set to make it do this.
EDIT: I may have made some progress. This site
https://enthusiastphotoblog.com/setting-up-sony-a7riv/ recommends setting AF-C and flexible spot tracking. I've tried this and it appears that when I focus on something and half press, it locks the focusing point and if I move the camera the point stays on the original focused object and the focusing box moves around the screen to compensate. Not only this, if there is a person in the frame, AF automatically finds the eye and locks on this even if you wave the camera around. This is pretty cool! Welcome to the 21st century, Dave!