How long would a no-bake cheesecake last?
I wouldn't keep it more than 3 days, 5 at the most if I was desperate for some cheesecake. I agree with your statement though I have never had a no-bake cheesecake last more than a day in my family. 

You could freeze it and I have tried with a piece, not a whole pie before and mine turned into cheesecake soup when I thawed it and tasted terrible. I am by no means an expert freezer of food though.