Isn't that only a risk if you need to sell the house at a time when the value is below what you paid?

Buying houses for shorter terms is just more risky, period. The housing market can crap out in catastrophic ways. Just like the stock market. The risk aversi

It would be an unrealized loss if you were living in a house with a mortgage bigger than the value of the house, so long as you pay though, you've still got a house to live your life in.

There isn't though, this calculation doesn't consider valuation of the home at sale time. What this considers is, how much could that money earn you in investments vs how much will you save in interest payments over the life of the loan.

What this does assume is that you'll live in the house long enough for the interest savings to catch up with investment gains.

that's not really part of the equation.

If you make the minimum down payment, and the value of the house drops, you're still on the hook for the full value at the time you took out the loan.

Once you've secured your mortgage, your payment plan (and therefore debt) has nothing to do with the value of the house.