Why do the transform tools change layer blending mode during transformation? If I have a layer in, let's say screen mode, and transform it, I would like to have it in that mode to see the instant result of my transform.

Because it the transform tool shows a preview on top of the canvas; showing a preview inside the layerstack would make the tool prohibitively slow.

Can't it just copy the blending mode of the current layer for the preview then?

No, that's not possible either.