Your math is perfect and the logic is solid.
However, there are real risk implications related to the more-than-20-years of mortgage-free living. When you have a rental with a mortgage, you have a 100% burn commitment for that income stream. If you don't have income coming in, you've still got to pay it. A smart investor keeps an emergency fund to handle any potential dips - and some people like the feeling of knowing they have to stay hungry to keep the place filled. However, it's a risk. Is it worth the $1,000,000 difference? It's probably heavily dependent on the rest of the financial situation.
My opinion is that you're absolutely right, but the scenario merits consideration of the investor's individual capacity for risk tolerance.