That's because, most of the time, GPS is nowhere near as accurate in the vertical. If the display was the same resolution, it's would change all the time, each update, even driving down a nice flat road, or sitting in the parking lot for that matter. This is due to something called "geometrical dilution of precision". It affects all the position components, but it take a really bad/unusual set of satellite geometries to make it bad in the horizontal, but it's not at all rare to have the visible satellites mostly out near the horizon, which means they are nearly in the same plane as your local horizontal plane. Which means the measurements are relatively bad normal to that plane, IOW in the up/down direction.
Now, that’s about as rational an explanation of the “Z-problem” as I’ve seen! Thank you!!