According to Logitech's harmony support page for PS4, Sony doesn't allow 3rd parties to power on the PS4 via bluetooth. This seems arbitrary and really annoying when we're trying to setup a nice media center with a single remote.
This support exists on PS3 but not PS4 so it does not seem to be a technological limitation as both are using Bluetooth.
Harmony articles that mention Sony being the limiting factor:
https://support.myharmony.com/en-us/harmony-experience-with-playstation-4
Harmony article about PS3 that says it can power off/on no problem:
https://support.myharmony.com/en-us/harmony-experience-with-playstation-3