My PS4 turns on and off with my Harmony Elite. All you need is this: https://www.amazon.com/PlayStation-Receiver-Logitech-Harmony-Control-4/dp/B01K3VMBM0

First thing: I genuinely heartily recommend you buy a PDP Gaming IR Receiver. Yes, I know the outlay is a pain in the ass when the only function it really adds is the ability to power on the PlayStation - but it really does remove all of the headache of trying to get HDMI-CEC and Harmony playing nice together.

In regards to your config - when you power off a CEC enabled device - it sends a "source shutdown" message via HDMI.
The receiving device makes it own decision as to what action it performs when this message is received. My Sony TV defaults back to TV input - obviously your LG is different.

Have you checked your LG TV's config to find out if:

• You can specify what the TV should do when it receives a "source shutdown" message?
• There's a default input on start-up you can specify?