This feature would be helpful to many, myself included.
If it has not already been mentioned, the auto favicon generation sometimes leads to misleading icons when web apps have redirects/forwards for OAuth. Example, a login page that automatically redirects to insert_OAuth_provider_of choice_here will show the OAuth provider icon, not the actual web app icon. An easy workaround (easy for users 
) would be to allow custom icons or change of an icon on an item. Side note - If I should report this as a bug please let me know and I will be happy to do so.
Here’s hoping this can be somewhere in the roadmap in the near-term.
Best regards.