I didn't see any reference to assume any stability
I did say
unless the wind continues to change
Yes you can be climbing into an increasing headwind, in which case the performance increase will stay, but the question actually said about a wind on the approach, normally here I would expect once the wind has gone round to a headwind it would then fall off as you get nearer the ground and so you will actually then lose performance. (And I will bang my head if I want to
)