Let's say your home is currently worth $200k and its payed off. Let's say you take that $100k mortgage and invest it. In the future there is a recession (or a a foreign war) and the market tanks - you're investment loses 50%. Then the bottom falls out of the housing market to the tune of 50%. Now your home is fully mortgaged (no more equity) AND you only have $50k in assets. You're so screwed it ain't funny.

I think the wise thing to do if you decided to do this would be to take a few bucks and invest in a tent - so you don't have to scramble for one when you become homeless.