The new imagined lens would appear zoomed (with say a 28 mm lens instead of 4 mm, which would be around 7x zoom, which is a real actual zoom by the longer lens). And it will be a lot of pixels, but it will still be a very small "cropped" image of tiny area, with crop factor of about 6x. So it would have to be greatly enlarged about 6x more just to view it at the same regular viewing size as full frame would need.
And enlarging 6x more reduces the viewing dpi to 1/6 dpi. The full frame image would have to be enlarged about 9x to view 8x10 inch size, so this tiny sensor has to be enlarged about 9x6 = 54x to view 8x10 inch size at 1/6 the dpi.
If using the same lens, the APS-C "appears" zoomed compared to the full frame image, but it is just an illusion. The lens image (from the same lens) is of course exactly the same image (just cropped smaller). It only appears zoomed after it has to be enlarged 1.5 or 1.6x more to view it at the same viewing size as the full frame. This extra enlargement fools us and the smaller camera costs less, and we like it, but the full frame image outperforms it, which is why you see the pros at the football sidelines using very long lenses on full frame bodies.
You can also simply zoom any existing image in the photo editor to see the same enlargement illusion, but enlargement costs dpi.