Don't get me wrong, I love having push notifications. But I was wondering how hard it would be to give each one the per-site icon so it's easier to distinguish between sites. Inbox By Google does this well, as it has the icon of the sender (from contacts, the address, or a fallback letter) as the large icon and a small Inbox app icon in the corner. Since sites without a custom icon default to the SE one, would that make it easier to implement?
And for consistency, perhaps the same could be added to the iOS version, although I am less familiar with how its notifications can be customised.