Umbrella policies that exceed your net worth are extremely cheap insurance (about $200/yr per million insured) against catastrophically sized insurance claims against you. They also have the benefit of automatically making the insurance company's lawyers, who I'm not paying for, start looking at the claim seriously when the threshold for the umbrella policy kicks in, or at least mine does.
Also, if I lost my job in 2008 when the housing bubble burst (oh wait, I did), my "liquid assets" in the now crashed stock market would be sold at a 40-50% loss to continue to pay my mortgage. On that same note, my 12 months (my personal comfort level) of expenses in savings are now much lower because I don't have a mortgage. This freed up money for investing rather than sitting in a useless (in terms of interest earnings) savings account, which now has an extra 12 years (time if I had made minimum payments on the mortgage) to earn compounding interest at a higher rate than my original mortgage rate. Further, I now have lower expenses and can generally invest a higher percentage of my income into appreciating assets.
Think of it this way. How many people in this thread would seriously advise me to take out another 15 year mortgage on my current residence, put that roughly $185k (because paying PMI is stupid on steroids at this point) into the stock market, and begin making mortgage payments again? Not to mention the mortgage payments will require me to lessen the amounts I'm putting into my investment accounts over that same 15 year period. Finally there's the intangible peace of mind that comes with not being in debt. Seriously, is taking on debt enjoyable to some people? Sure as hell isn't for me.