I'm sure it would be possible to have VR ON during composing/focusing and OFF during the actual exposure, it should be just a matter of programming. Whether Nikon think this is a sensible thing to do is another matter.
I find that VR SPORT with the 300/4 PF does work nicely also for faster shutter speeds (typically 1/500s to 1/1250s in my case with this lens); I would turn VR OFF at 1/1600s or faster. Hand-held of this very lightweight tele is much easier in VR SPORT mode than VR OFF. But VR OFF may result in sharper pics (and perhaps fewer artifacts) in some circumstances.
Hmmm, I use VR Sport essentially all the time, even up to 1/5000.
Indeed, it does help frame the capture, and I've never seen it blow the background out like what's described.
I've read that
early versions of the 300 PF exhibit this effect, not late ones.
Another variable is the D850 and "its" compatibility with the 300 PF.
I use the D500, and I honestly think the D500 was "made" for it. I have got 'perfect' bokeh with the 300 PF in "Sport" mode from 1/1600 to 1/5000.
Here are some examples ... all very small birds ... all images cropped to some degree. Still decent bokeh: