The importance of gripping using ones thumb.

Now call me old-fashioned but can someone explain for my feeble mind what the advantage of not gripping a rifle with your trigger hand thumb is but instead resting your thumb along the stock?
Any videos I watch now seem to have this err… non-grip and I note that often the rifle recoil throws the loose hand off the stock completely which must really, like really help a quick follow-up shot….
In the second pic the shot has just gone and not only is the hand off the stock but the trigger finger has come clear of the trigger housing!