FWIW I'd leave the router always on because I've known power supplies
to die when being
switched on/off all the time, maybe someone who knows electronics can
say why.
It's the thermal expansion / contraction which puts stress in the soldered joints / chips etc.
Switch on and it heats up a bit and expands. Switch it off and it cools down and returns to the normal size. Repeat and it stresses all the components. Like you can bend things (ie a used drinks can)several times but do it too many times and it breaks.
HTH Keith