Yes indeed, reading Height Above Terrain with a resolution of a couple of feet is not accommodated by the classic aircraft instrumentation set, particularly not the set in aircraft used for initial training.
Learning how to fly is for a large part training the body to control the visual and motion sensory inputs. Not every aeroplane has a HAT instrument, so it is not a bad idea to get trained in making an assessment just based on out-the-window view and the feel of ground effect kicking in.
Reading an instrument takes more time than feeling and seeing motion, and time is critical when touching down.