That ugly thing to the bottom left-hand corner

[Niwashi]

You can. Right click the general tab and click Hide Log Window

This only temporarily hides it, though. I'm not sure about keyboard/mouse players, but controller players cannot select any other HUD element or alternate between windows without bringing the chat box back up. (Clicking the touchpad cycles between HUD controls and active windows, but the first one selected is always the chat box, bringing it back up if currently hidden.)

I know I've minimized the thing a few times when the trash talk enters the xxx beyond explosive.
At some point it just becomes a distraction and you just have to stop looking at it.

If the annoyance is limited to a particular channel, a better option can often be to just remove that channel from the active tab you generally watch. You can put it on one of the other tabs if you still want access to it at times, but without interrupting your gameplay.