There is a difference with "Control Points" that you show and "Geometric Points" like in PolyModeling...

Else you can align Control Points of only one separated surface! (Transform / Align)

So your face face must be have many separated surfaces! :) a little nightmare !
Or Maybe your face is yet only one surface ?

You have better time to use some cool free easy prog like https://stephaneginier.com/sculptgl/ online
Then use Free Instant meshes for have quasi only quads and then SUBD Create From File inside Moi !