I have a question regarding the chat cable. I have one also and whenever a press L3/R3, or tap controller, the "speaker" icon shows on screen as though I am talking (even though I am not) - same with PS4 mic that came bundled with system. Do you notice this issue?
The Turtle Beach XP Sevens I find amazing with the mix amp and can connect your phone to chat off line or take calls. Similarly Turtle Beach XP51 does all that wirelessly only having to be connected to the controller.
Headphones allow for...
Listening as loud as you like without disturbing anyone else in the house (or beyond).
Far superior sound and clarity over any tv speakers I've ever used. This applies to even "budget" headphones I've used... Honestly, using some earbuds plugged into the DS4 is better than listening through a tv.
Use of a mic without making everyone else listen to your game broadcasting to them via the chat channel.
Functional surround sound options for a fraction of the price a good surround sound stereo would cost and without all of the setup/installation headaches.