This is a suggestion for the mobile clients, for Android and iOS versions.

Add an option to enable the display of multiple panels. This would be especially useful when used on tablets which have a lot more screen area.
Could have a section where the user can select different panel arrangements to best fit their particular device and screen. Such as a 2 column, side by side arrangement showing the channel list panel and the chat panel. Or a 2 row arrangement with one panel above the other.

For example I use TS3 on my Maven Pro 11" tablet and when viewing the channel list in landscape orientation, the list only takes up about 25% of the width of my screen. That leaves 75% of unused screen space which could be used to display text chat. Even when I switch to portrait orientation, there is still a large portion of my Maven's screen which is unused.

Even on my smartphone, I sometimes wish I could display a small version of the text chat panel at the bottom of my smart phone's screen below the channel list.

The idea is to provide the user some more control over how TS3 is displayed on devices with a large screen so they can display TS3 in a way that works best for the user and their device.