It is a limitation of a PWA. A native app (wrapper) will likely be coming though, and a custom Capacitor plugin could theoretically interface with the native API to switch out icons.
Do you already have an idea of how the result might look like? Is it just going to be a web view, or could it actually take advantage of native functionality such as e.g. the back gesture, haptics, scrolling hiccups, scroll-to-top etc.?