I use the AF-On only pretty much exclusively. Hand held or tripod - makes no difference. That way, focus and shutter release are always two separate thought processes and actions on my part, which gives me the level of control I want.
As an example, on a long exposure on a tripod, normally I need to close the eyepiece shutter first to block extraneous light from the meter. But before I close it, I want to know that I have locked the focus, and when I press the shutter there is no chance of the focus changing since I can no longer see through the viewfinder.
There can be situations where using the shutter to do both is needed, like capturing timid wildlife that will not come if I am around. I set up on a tripod, hide somewhere with a wireless remote, and wait for the animal to come into the frame. Unless I know in advance exactly what distance they will be from the camera at that point, then I do want to focus and release the shutter with a single press of the button. But these are by far the exceptions.
And finally knowing me, if I started mixing the occasional use of the shutter doing both, I would end up screwing the focus up - forgetting that the camera will refocus when I press the shutter, because I am so used to the AF-On only method. I need to keep it simple!