They are actually not commodity hardware. The PlayStation and Xbox CPU/GPU is custom built for the console. Try finding a CPU that can use GDDR RAM!
I should be able to put in a Linux DVD or memory stick and install Linux on it.
Or at the _very_ least an alternative app store.
IMO it's pretty arbitrary. I wouldn't expect to run software on an appliance, even if the underlying hardware is commodity. And an appliance is something that performs a specific task (fridge, car, etc.). There are gray area cases though when an appliance does more than its basic function (smart fridge, car infotainment).