indeed it seems it has been a long time since favicons are not displayed in Intranet or Allip modes. The reason is in the code producing the favicon URL itself
so I think you won't be able to do much more, unless fixing it. I think the condition is wrong and should check the result URL protocol is http instead of checking whether we are not in Intranet mode...
I will have a look at this and probably push a fix soon.