The crop factor needs to be applied to the FoV, DOV and the overall light gathering ability. of the body-lens combo. In real world usage the light gathering part can be disregarded, because the camera manufaturer already applied the crop factor to the iso rating of the sensor, to make the same iso number look equally bright on different sized sensors. This is provided we are talking about two sensors of different sizes but the same pixelcount.
The sensor size is irrelevant to exposure. The manufacturer calibrates the ISO settings due to differences in light-gathering ability of differently-sized photo-sites which come from the desired pixel density of the sensor as it is the size of the photo-site that determines how much light is gathered per pixel for a given light intensity. That is the only variable, they don't calibrate by sensore size.
The example I gave above of a camera with an FX sensor with a crop mode illustrates this. The pixel density of the FX and DX areas are identical in pixels/sqmm so the exposure settings do not change depending on whether FX or DX mode is selected.
A 200mm/2.8 lens puts out a given light intensity to the projected image circle. That light intensity does not change depending on the sensor/film size (assuming zero corner falloff and the circle covers the sensor/film).
So the lens manufacturers list their lenses correctly. A 2.8 is a 2.8 is a 2.8. Yes they have different DoF effects but that is not the prime reason an f-stop is quoted for a lens, it is to tell you about light gathering power, not the DoF side-effect. To quote a 2.8 lens as something else relating to DoF would be to cause a bigger error/uncertainty than that being "fixed".