Hi Kent,
I must admit that I was stumped at first by the fact that Mixing the Vector Coordinates before the Noise Texture didn't work; I would have wanted to do that as well.
Basically, the two vectors cancel out in the middle of the transition. I will add an image next (can't add one directly under a lesson) to show what's happening mathematically.
If the transition were also Linear, instead of Bezier, the Vector, and therefor the Noise pattern would even be constant!
Thanks for posting this spikeyxxx. It's very helpful to see supporting math for why this doesn't work the way we'd expect