Is cutting the power off monitor safe, without actually turning it off

My power button in my LCD Monitor is starting to not work   When I press it, it won't turn on my LCD Monitor all the time... So I have to press it until it does. The same goes for Turning it Off.

I think that it might at some point come to the time that I won't be able to turn it On at all because of that.

So I came into Idea of not turning it off Since I cut the whole power from it when I turn off my PC.

My PC and monitor, router, speakers and modem is connected to something like this -> http://www.leroymerlin.pl/files/media/image/850/1144850...

I have no idea what it is called in English so I've posted an image of this.

When I turn off my PC, I usually power off my monitor on it's power button, and then turn off my speakers and Turn off whole power to all hardware with that button on that power thingy I've shown on the picture (you see that button to cut the power off on it right?)

So It came to me to instead of Turning Power Off on my LCD Power Button, I would just simply leave him running then cut whole power on that power thing, so All would be without power and turned Off (even the LCD)

My question is - Is it safe for lcd monitor to cut off power like that? I mean is it safe to just raw cut off the power off monitor without properly shutting it down on power button? Won't it damage it at some point?

I will be awaiting your respond to thing question.

PS: I've put this topic Under TV Tuner Cards sub-category, I know it isn't qualify for this category but it isn't for others as well and this forum clearly says "Displays" ...