Assume you rented a house for $2,000 a month. You own the home and it is completely paid off. You also live in another house that is also paid off. Would you quit your job (most likely a higher salary and benefits) to enjoy life and never work again for some money to survive? I would assume a very frugal life.
If I did that, I would actually end up being homeless. The taxes are super low in my state, but the average house tax alone hovers around $2k-$4k due to how expensive housing is over here.
This sort of situation is what you actually want to avoid OP - being house-rich but cash-poor screws you over more often than not. Better to have one house you can rent.