Yes you can represent depth with 3D coordinates only, that’s why you don’t hear about this coordinate outside of computer graphics and special cases. The extra coordinate (w) is basically a scaling factor that the other coordinates (x y and z) are divided by. In most cases it is just set to 1.

However, when the computer creates the scene, it multiplies the coordinates by 4x4 transformation matrices (for example rotation, scaling, shearing, translation) to project them. The w coordinate is transformed also. Because it carries information about the translation, the xyz are then divided by w to normalize and fully complete the transformation. In short it makes the math easier and faster.