You still need to rent something for you and your family. It's almost a fixed cost in your life. In any case, it's better to turn that fixed cost into an investment.
It's hard to believe you'll ever get your equation right. Even more when you weight investment risks and actual average ROI over 25-30 years in stocks.
What about property taxes? I know people who have paid their house off in full and still pay 12-15 thousand in property taxes each year.
Additionally, even if the house is paid off, you're still on the hook for all repairs, maintenance, etc. And if your neighborhood starts to go down the tubes, your house value can quickly decline as well.
What if Enron or Lehman Brothers utterly fail? What about taxes on stock gains?
I think property taxes in US already vary a lot from state to state. It certainly vary also from country to country. It's something you need to be aware to take a decision on whether it's a good investment or not.
Ultimately, all these costs are also embedded into renting price.