Dividng clip space by "w" warps the output?

Edit: Thanks to Bunny83 for the explanation. It seems I skipped an important piece of information about projections somewhere along the way and because of that I didn’t plan out my approach correctly.

so I’m writing a special effect and I need the NDC coordinates (the coordinates automatically calculated from clip space coordinates by graphics API). I read that what happens under the hood is a division clipCoord /= clipCoord.w, however, doing so in the vertex shader warps the result and does other weird things. Am I not understanding something correctly?

Images (upper / only warped image is clipCoord /= abs(clipCoord.w)):

WOW. I understood absoulutly nothing. This made me realize how much of a newbie I am…