I think you're being downvoted because the imprecision you speak of is a result of: consumer GPS receivers having a limited polling rate, limited precision, and only using one GPS frequency. You can't extrapolate the limitations of GPS on say a phone, to limitations on a commercial plane.

See the following from gps.gov: it can be accurate to within centimeters and with a high polling rate, but most consumer devices don't employ the necessary tricks. https://www.gps.gov/systems/gps/performance/accuracy/

Military gets more time resolution as well as no deliberate clock skew. Airliners won't have military GPS. Gps receivers for surveying require on the order of hours to resolve to "centimeters" using civilian GPS.

The highest resolution GPS receiver I have still has +/-15ns jitter, which over the course of a day is good enough for maybe 12-20cm resolution, but the first hour the track is wild, 50-80 meters off in varying directions.

My GPS is used as a time stamp source for lightning detection and location, so in aggregate with other detectors it can pinpoint a strike to within a meter or so anywhere in my hemisphere.

This is why a recently calibrated altimeter is used for the altitude axis on GPS approaches. They also must have a constrained error margin to be certified, and it is factored into the buffered region around the approach.