Why do we need tiling window managers when we have tmux?

I used to use Sway and I found tiling to be useful only when using multiple terminals. Tmux allows me to have tiling functionalities for terminals while having a full desktop environment for all other applications.

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I've tried hard to get libreoffice and dvddisaster to render in a terminal but for some reason it never works... 😏

You could probably get it to work in a framebuffer... 😏

Probably not though, although some apps like mpv, (maybe vlc) and mplayer can, plus QT and a GTK fork have support too.

Mplayer can render to the terminal using aalib

I guess if you have to use a classical terminal or terminal emulator, but I was more talking about drawing apps directly to the Linux console without X or another sort of windowing system.

For example this is Midori, a web browser:

Well yes I thought you were using emulators. When I was a kid I would frequently break X11 so I spent much of my time on the console framebuffer. All I needed it to to is let me watch TV and videos till I was bothered to fix the config file for X