Now, if weather alone was a primary cause in the case of AF447
I am going to be a bit of a nitpicker here. The intent is to assist with understanding.
"If
weather alone was
a primary cause"
If weather
alone was the cause, weather being the
sole cause, then there is no resort to primary, secondary, or tertiary causes ... but I think that the way your framed that isn't the right lens through which to view this aviation accident.
For what it's worth, I have learned over the years to look at aviation mishaps and crashes as being shaped by contributing factors, some with greater weight than others, but all being linked together in combination to provide
a combined cause for the effect, which is a crash or other mishap.
I invite you to consider the infamous Swiss Cheese model.
Colorado Firecamp - HFACS, the "Swiss cheese" model, Introduction
What you might be looking at is the issue of being necessary and or sufficient.
"Without the Wx as the trigger, would this mishap event chain have been broken?"
That is one way to look at it. Weather has been around us (and a hazard) since Orville and Wilbur took to the skies. How we mitigate the numerous risks that weather provides to the flying environment is one of many factors in flying safely. (You alluding to wind shear is a well placed example).