The advantages are great. Remotely controlling your lights offers more safety and is better for the environment. Furthermore, they offer a major convenience.
The safety issue is that when you are away you can control the lights in your home. This means you do not have to set the timer to turn lights on and off on a schedule. If someone suspects you are away, watching the repeating pattern will give that person enough information to know the house is empty. You can turn lights on and off more randomly, hence give no set pattern.
If you are out late at night, you can turn indoor lights on remotely giving the illusion that you are in the house. And, you can also turn on outdoor lights to allow you to return home to be to a well-lighted exterior of your house, making it less inviting for people who pose a danger to remain lurking. This is if the switch is located indoors.
From within the house, should you hear a noise, and be unable to get to a light switch without revealing your position, or putting yourself in danger, turn lights on from your phone. Once lights go on, the intruder will often leave, especially if several lights begin to go on one after the other. This implies you are not alone, and multiple people are aware of the sound, something unwelcome by a typical intruder. And, all the while you can be hiding behind a locked door, or have already exited through a window.
Another aspect of this device is to allow you to save energy when not using a light. You can just call home literally from around the world and turn off a forgotten light. This saves on energy, which today is the responsible thing to do.
As for convenience, imaging that you are comfortable in an easy chair, and suddenly you decide should turn a light off. Just dial from the chair and off it goes. I realize the exercise can be helpful, but if you must turn off a light from
during a critical time in a movie you really do not want to get up.