We have to react to what the plane is doing and from our perspective on the ground the plane is going to weathervane into the wind to maintain a proper ground track. That is the purpose of crabbing in the first place. That is the only point I am trying to make here.
Absolutely right. What's important for beginners to realize is that crabbing occurs because of what the pilot does with the controls while flying in the wind, not because of something the wind does to the plane or that the plane does "on its own." (Same for the other behaviors often attributed to wind, but those, like too sharp a turn causing an inadvertent roll, are mostly things the pilot doesn't really want to do, while crabbing is a good thing.)
To return to the OP's point (post 57), none of this says that the wind has "no effect" on a plane. A plane flying in a mass of moving air moves (relative to the ground) right along with that mass of air, so if you have a crosswind blowing straight at you when landing, the plane will be carried toward you, sideways, at the speed of the wind if you keep the nose pointed straight down the runway. The purpose of crabbing is to counteract this. But you, the pilot, have to make it crab.