F1 Toggle Not Working Within Container Objects

Similar to https://mojang.atlassian.net/browse/MC-2430

I know when you initially press F1 - it makes your HotBar, Text Chat, Levels, In-Game Pointer, Health, Hunger, Player's Arm, F3 Menu, and the item your player is holding... all disappear.

When you then open up a container object your health, hunger, hotbar, Text Chat, and F3 Menu all display in the background behind the Container and Inventory GUI.

I also know that you all said in the other report - that it works as intended ... and I actually understand that - I mean it would be horrific if I couldn't see the items in my hotbar to move them to a container - especially If I was recording a video or something. However, the GUI's all include their own hotbar and player inventory in it's own inventory.

What I want to know is - what about everything else too? Is it necessary to display the levels, health, hunger, F3 Menu, and especially the chat while F1 is enabled (and) looking inside a container object.

Side Note: My main concern was mainly chat, levels, health, and hunger - I wouldn't mind if hotbar shows up - but if the GUI's include their own hotbar, do we need it?

The container objects - where background hotbar and etc. show up:
Anvil | Crafting Table | Chest | Inventory | Brewing Stand | Furnace |
Beacon | Horse, Donkey, and Mule Inventory | Dropper | Dispenser |
Ender Chest | Enchantment Table | Item Hopper |
Storage and Hopper Minecart | Trapped Chest