Mine only powers up as you describe.
I know what you mean, I kinda liked the old factory sony unit features where you could power on without key in ignition and it would light up when you buzzed the key fob.
Not sure if there is anyway around this, maybe a wiring issue which is a bit beyond my scope.
I am happy I bought this unit though and to be honest its worth this small sacrifice for all the other features that come with this unit and it looks the nuts in my focus without blowing my own trumpet lol :-)
Mine does the same also another thing it does is with the key out when I open the drivers door it powers up lol
and switches off when I close door
Anyway I'm still pleased with it tho love it