I believe you flipped things, PPD does change based on distance, DPI does not. This change based on distance is a feature since when you're really close to a screen it does lower the visual clarity.
Maybe it would help to think of PPD as a measure attached to the viewer, while DPI is a measure attached to the display device or screen.
When a projector shows something at 100 PPD on a curved screen, and you make the screen bigger (moving it further away), it’s still 100 PPD to the observer sitting near the projector (even though the DPI on the screen is lower) - the observed resolution stays constant regardless of distance, because that’s what pixel per degree is measuring- observed resolution.
When a flat monitor screen is 100 DPI, it says nothing about the observed resolution. Moving closer to or further away from a constant DPI display changes the observed resolution. I wouldn’t necessarily call changing based on viewing distance a “feature”. It’s a byproduct of that unit of measure, but the answer to the top comment’s question is that PPD is an improvement over DPI when the question is what resolution does the viewer see. DPI is mainly used because it’s easier to measure, and it’s good enough in practice if the display in question has a narrow range of sizes and typical viewing distances, like monitors often do.
One DPI, is a measure of what detail can be displayed on a given display and does not speak to whether a user can actually see it.
The other PPD, is a measure of human acuity and speaks to detail that can be seen regardless of distance.