Shots mean something.
Scoring chances and chances in the high-danger areas certainly speak more to scoring threat. But having the ability to shoot, retrieve, shoot, retrieve, etc, doesn't just speak to the ability to shoot the puck, it speaks to all the plays made between, all the little battles won, all the quick decisions, that allow them to keep getting the puck and putting it on the net.
And if you have a high shot differential, that speaks to not only the ability to fight for and retrieve the puck, it speaks to an ability to prevent the other team from doing the same.
Where did you see the numbers for high dangers chances separate from xGF out of curiosity? I'd like to see them.