When choosing "Add to Home Screen", it would be useful to apply a custom image for the icon.
The use cases are for this feature on mobile would be identical to Orion on desktop, where it's already possible to customize PWA icons, including differentiating visually from the official app, if installed.
While useful just for fun, I've also found that certain websites do not show an icon at all. Saving discord.com/login for example just shows a white "D" on a black background as the icon:
