That's an awesome question!
The influence of IoT in power saving wouldn't be that huge!, as you've mentioned.
But making them smart enough would save a lot of energy.
The radio system and the whole automation system would consume only about 5V-1A(Max) if there are no motor drivers and other power components involved(in the case of lights, there are no actuators!).
The consumption of a bulb will be quite large(in fact fact multples) compared to that of the IoT system.
So, if the bulb is on for another 5 minutes without being noticed, it would consume quite high amount of power than the IoT device may consume day long!
Connecting to the internet can still increase the efficiency because, the sensors would be used to check weather the person is inside using motion sensors, or sensing the door. Which can actually malfunction.
eg: if the person is inside and idle, the light goes off (Guy gets annoyed). or if the guy is out and the door is open and there is some moving object in the room, the bulb still glows!(Lot of energy gone)
If the device is connected too internet, the Guy's phone would have the necessary app, when he goes out of the house, the phone knows he's out and the whole home will b off (configurable).
I have very less idea about the particular products you are talking about because, I have not used either of them myself!
IoT is very much controllable over the internet. Far more than the power consumption it is customizable is what makes it stank out!
