Yes, it does change, but not if you are "seeing" it as purely an image that is being shrunk. You have to try to imagine that you are looking at a real scene, not just at a two-dimensional photograph.
It is often easier to imagine that you are looking at a real scene when viewing a moving image. Have a look at the second video in this article. Zooming the lens is the same as shrinking or expanding the image. When the lens is zoomed back to a shorter focal length the image is shrunk. This makes the distances from the camera appear greater, so the train appears to be moving faster.
Most people see the illusion of the train moving faster even if they do not consciously "see" the distances increasing when a still image is shrunk.
Another situation in which the perspective seen by the viewer is particularly important is the rear-vision mirrors (or cameras) in a car. My car has four: one mirror at the top-centre of the windscreen (which gives a normal perspective), two side mirrors (which give wide-angle views) and a rear-view camera for reversing (which gives an ultra-wide-angle view). The wide-angle views make things appear further away than they really are and the driver needs to make allowance for this when reversing.