While the effective field of view on a crop camera may be the same as a longer lens on a 35mm, the focal length does not change and therefore neither does the aperture. A 17 - 55mm lens may give the same FOV as a 27 -88mm but it's still a 17 - 55mm and the relationship between the first element and the focal length remains unchanged as does the aperture.
You're right, but what is your point? The focal length just gives the image scale. 50mm/2.8 on FF gives exactly the same field (solid angle) as 80mm/4.5 on 1.6x APS-C (barring lens distortion). The flux of incoming photons per solid angle will be the same. The DOF will be the same. If the detectors have the same number of pixels with the same sensitivity (say fraction of photons actually detected, also called quantum efficiency) and read-out noise, dark current etc, then the resulting image will be statistically identical in all respects.
The lens is just an optical system to capture photons and compress them to a small image. The advantage of FF sensors is not that they are inherently more sensitive. The advantage is that it's easier to make optics that produce larger image scales (e.g., it's easier to produce a good EF 80mm/1.2 lens than an EF-S 50mm/0.75 lens).