Customisable Chat Window as Overlay
The stream viewing options on desktop include "fullscreen" (no chat displayed) and "theater mode" (chat occupies about 1/3rd of the screen, on the right). Given that the vast majority of streams are in widescreen format, dedicating a large vertical column to chat results in the gameplay "window" occupying less than 1/2 the screen, with huge "letterboxing".
It would be a huge improvement to allow the viewer's chat display to overlap onto the video feed, via a window that can resized, repositioned and whose background can be made transparent. It would serve as an "interactive fullscreen" mode, where viewers can be immersed in the gaming (since it fills the screen) and also follow chat to whatever extent they desire (some may shrink the window and have just the last two entries overlaid in the top-corner of the stream feed, others can have a long narrow column of chat, etc.).
I find pop-out chat to be a poor substitute for this type of functionality ~ it's easy to dismiss accidentally, has large needless borders and cannot be made transparent.

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Night0wI commented
I absolutely agree with this. We need a way to have a (sleek) chat window in fullscreen.
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SaintInigo commented
This would be really cool. Honestly, any way to enable/disable chat in fullscreen mode I feel is needed.