Thieving might be used for the above exposed purpose (plating, wrapping, etching, etc), for internal layers it has the simple purpose of keeping the PCB thickness uniform across the PCB area. Indeed the PCB manufacturing is using heat press action to stick together the different material layers (core, prepeg, copper, etc).
In order to have the compression force uniform across the area and independent of the material layers you would need to have each layer filled uniformely with material of the same elasticity. But this is not the case because PCB track will be seperated by the prepeg material of the insulator layer. So if you have a large area of an internal layer without copper, the prepeg layer above this copper will need to fill up this empty space.
So if you have areas where layers are empty and other areas filled, the manufacturing process (heat press) will create different pressure across the PCB, creating different thickness across the PCB area. The difference can be significant and it all depends on the thickness of all internal prepeg, hence depending on the copper thickness, PCB thickness and number of layers.
This is why in the picture you provided the large space (too large) is filled.