Honestly I do not understand whether you're asking why is the LTE considering the camera, or if you're asking why the LTE is not considering the camera.

Same for me, but i think a better example for the question is:

Taking a pictuture of a white wall, euqually lit over its entire area, why are the corners of the picture darker than the center?

I've found this wikipedia page about that: https://de.wikipedia.org/wiki/Cos4-Gesetz

But i don't know how to get the english version. (There is one about vignetting, but vignetting is the wrong term and has different reasons)

I think this cos4 law is the key to my questions.

My guess is that to avoid vignetting effect, the We factor (importance function) is proportion the inverse of cos4. And since the pdf of primary ray contains cos3, it just gets three of the four cos cancelled out. And the left one in the denominator gets cancelled with the cos factor in the LTE, hidden in the G(v_0 - v_1) component.

I've checked the pbrt-v3 implementation, it works this way.

https://github.com/JerryCao1985/pbrt-v3/blob/master/src/cameras/perspective.cpp