If I don't use XOR in Davies–Meyer, does it remain collision resistant? If I don't use XOR in Davies–Meyer construction like in picture 2, does the function remain collision resistant?
Let $h=E_{x_i}(z_{i-1})$ in your suggestion. Let $z'=E^{-1}_{x'}(h)$. This gives a collision between between $(x_i,z_{i-1})$ and $(x',z').$

The XOR makes this attack difficult.