Sure, but even then it’s also connected to IPS’ implementation. I upload an “application icon”, which is fine for this very purpose, but this is also downscaled and suggested as generic image. But that image might not work at all at tiny sizes. At least in this case, it would be necessary to force a dedicated small image. And in fact, that’s what happening for the ACP where you don’t output the full line of images.
In other words: the problem is that the application icon is not just suggested as application icon in the generated code.
If I remove the application icon, I get the desired result for the favicons, but then I do not have an application icon for when the website is saved to the homescreen.