Nope. Its mine and husband's. They just get to borrow it from time to time
I can't tell if that's sarcastic or not, but if so, I don't quite get the point - sorry.
They can play in the living room without storing their toys there. That is what their room is for. Storing their things
So do you have a completely empty living room, then? Do you keep your telly, PC/laptop/tablet/phone, books, ornaments etc. etc. in your own room, bring it to the living room to use or look at it and then take it back again out of view?
Children don't just play with toys to make a mess or annoy you - they're how they learn, communicate and are entertained, just like you are with a telly, laptop, books or whatever.
You run your household the way you think best, but I personally would hate to think that my DS might grow up feeling that we tolerate him, blame him for being a child and resent his very presence being observable in the home that is for all of us in the family.