Dave Ramsey, who, for lack of a better term, one might describe as a "personal finance turn-around guru and radio personality", poses the question you ask in a different way. I paraphrase: "If you owned your house outright, would you go out and get a mortgage on it so that you could invest in the stock market?".

Financial management is about much more than maximizing returns. It's also about managing risk. For most people who have assets that they will depend on in the future, managing risk grows in importance as they grow in age. Taking on debt (a mortgage) in order to make speculative investments is a high-risk endeavor.