You can turn your internet router off at night if you want too which can help protect your network from possible hackers that may try to intrude into your network at night.
But other than that there's not much other reason to turn your internet router off at night and it just means that there will be more wear and tear on the router when you turn it on and off repeatedly at night and in the morning.
The internet router also uses very little electricity that it will not be worth it to save the pennies that it uses while on.
You also have the inconvenience of having to turn the internet router back on every morning and waiting for the internet connection to establish through the WiFi.
Me personally I never turn my internet router off at night but will turn the router off if I'm away from home longer than a day.
This helps prevent any potential hackers and prevents possible issues should the router suffer from a power surge etc.
I unplug the router when away from home longer than a day.