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. And there is the need for the human to teach the body how to land, pick up landing skills as mentioned in @MichaelHall's answer.
Indeed, autoland touches down algorithmically, with higher repeatability than when humans land. Basis of that are transmitters of signals that we humans cannot pick up, the receivers in the plane can. And now, what we do not want is that the plane can only touch down when the signal receivers are working properly. As ever, in civil aviation the three most pressing factors are safety, safety and safety:
- Civil aviation is super-safe, but of the relatively few accidents the highest proportion is in landing. From this link:
Nearly half of all worldwide commercial jet airplane accidents during the 10-year period from 2004 through 2013 occurred during the final approach or landing phases of flight, according to statistics published in September by Boeing Commercial Airplanes.
- Fully automated flights with no pilots on board are not perceived well with paying passengers.
- And humans must be able to take over in emergencies, as mentioned in the answers to this question. Captain Sully in the Hudson indeed.
Yes there are algorithms that can land an aeroplane deterministically, but well experienced skilled humans must be present to take over in an emergency and get us safely on the ground when the avionics systems are not in order.