If all of our perceptual constancy was lost, functioning would be quite difficult, if not impossible. There are too many problems to list them all, so I will cite one example.
We would lose our depth perception, as one the things it depends on size constancy is one. If we were no longer able to perceive the size of an object as unchanging despite changes in our relative position to it, we would not be able to perceive how far from us it is, what orientation it is in, whether it is moving. Driving would be impossible because we would be unable to keep track of other vehicles on the road.