> The PS4 doesn't allow anything other than a PS4 controller to turn it on.
That has changed. Both PDP Media Remotes for PS4 can turn a PS4 on. Still proprietary, but they're technically not PS4 controllers.
Reading from Amazon reviews, also the PDP PS4 IR Receiver For Logitech Harmony Remote Control Devices can turn a PS4 on. But I can't confirm this as I don't own one.