I'll throw in my opinion... which is a no..
As AC say routers and the exchange are adaptive and they learn from each other what the maximum speed is achievable over your line, this process can take anything upto 10-14 days when you first connect the equipment and turning off your router resets this learning procedure.
If you turn your router off every night then it will never full learn what connection speed to use and you may end up either running a lot slower than it could, or worse, faster than your line can support and you will have instable broadband.
Leave it on... it's how they are designed to be used.