But an ef 35mm lens projects the same image behind it regardless of the sensor behind it. If I take a head shot with an ef 35mm lens, then change to a 200mm lens, back up to the same framing, they are different images. The 35mm lens' subject will have a bigger nose. So, an ef 50mm on a crop is different than an ef 80mm on FF. Maybe something was lost in the ether, but 50mm is not 80mm.
That is because you changed the distance to subject in your example. If you stand in the same spot and take a photo of the same subject, the perspective will be identical with any lens, save for any distortion introduced by the lens (ie field curvature in a fisheye lens). Of course the framing will be very different, though cropping to the same framing will overcome this (though will not result in the best picture quality).
Apply this to a 50mm and 85mm lens, taking a portrait, and you get a perfect example of why we use equivalent FOV's. Put the 85mm lens on the FF camera, and take a photo. Now put your 50mm lens on that same camera and take another photo. The perspective will be exactly the same, but the framing is different - you have a whole bunch of extra area around the edges of the image. But, if you crop that 2nd photo to the same framing, it will have the exact same perspective as the first photo. Now, pair your 50mm lens with a APS-C camera. It will give the same photo (in terms of perspective and framing) as in photo 2, although it is already cropped straight out of the camera. The FOV will be the same (give or take a few mm), and the perspective will be the same, as the photo taken with the 85mm on the FF camera.