Automatic landing systems rely on ground support by way of microwave signals from transmitters installed near autoland-capable runways. There's no general position information, and the airborne part of the system can't operate independently of the part on the ground.
Civilian GPS signals are limited in terms of position accuracy, too. I believe the CEP is ten meters. That's not bad, but it's not good enough to land an aircraft. Altitude information from GPS is (IIRC) either nonexistent or severely limited, too. About any aircraft with a glass cockpit is going to support a moving map display, and those do see use - but, as a couple of professional pilots in this thread have noted, during final approach the main concern with regard to aircraft position is relative to the glide slope and the runway, and a moving map has nothing to do with any of that.
On a more general note, it is remarkable to me that so many otherwise apparently sensible software engineers seem to regard aviation as a problem trivially susceptible of perfect solution - every time we here on HN discuss any sort of mishap even peripherally involving any aircraft, the same suggestions invariably arise around automation, various schemes of runway lighting, cockpit lighting, instrument augmentation or replacement, pilot augmentation or replacement...
One would tend to imagine that the history of our attempts to perfect our own craft - including those attempts which we who build and maintain software make anew every day - would give us cause for humility on the subject of fields other than our own, about which in the main we know next to nothing.
Imagine five hundred airline pilots confecting an ad-hoc, long-distance postmortem
of the recent us-east-1 incident! You'll have to imagine it, because it did not happen - and it is rare at best in my experience for pilots, because they are skilled in one highly complex and technical field, to imagine they can speak authoritatively in the context of another. Perhaps we might profit by their example.