"(1) Do you agree with the idea that, despite not having a mortgage, my house is a liability? I’m not suggesting that a debt free home is not a justifiable liability, but just that it IS a liability.
(2) Does it make sense to put the equity from this home to work for me and use the cash to buy more assets, even if it means taking out a mortgage and increasing the magnitude of the liability?"
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The only person who can answer those question is you, and anyone who says otherwise is a liar.
The answer depends on what amount of risk YOU are comfortable with. If you want to say "This is mine, and no one can ever take it from me," then better to own a hovel free and clear than a mansion hocked to the gills that keeps you awake at night. If you can sleep like a baby while the wolves circle, then maybe you are okay with a leveraged mansion. That's number one.
You talk about building wealth, but how much wealth do you need? Specifically; How much money do you need by X years of your life in order to live the lifestyle you want for Y years thereafter? Only you can answer that question. Once you do, you need to figure out what return on your assets is needed to reach that amount of money by your X birthday. Examine the options and invest accordingly. It does not need to be in real estate. Or maybe you want part of a syndication deal in real estate, who knows? The important thing is to find out your ROI needed and balance that against the risk levels you are willing to take.
Then there are life choices. Plenty of people could invest elsewhere and make as much or more money, but they choose to stay in their community and help turn it around. Similar situations abound, I am sure.
There is, however, an iron rule of investing, with no exceptions. When evaluating your options, consider:
Safety
Income
Growth
-- chose two.