Because of the federal real estate capital gains exclusion of half a mil, 20% marginal long term cap gains tax rate, and the difference between historical real estate appreciation vs SP500 returns being maybe 2% at absolute most, an average rate of increase of about 5% on a house, the average transaction cost of obtaining a mortgage is maybe 2% (stock transactions are practically free in comparison), S+P return after inflation is about 7% the median duration of owning a house being about nine years, extremely sloppy back of envelope calculation for $200K would be (200e3 * 9 * 0.07 * 0.8) - (200e3 * .02) or 96K for owning more stock with a mortgage for $200K and a 200e3 mortgage at this time would cost 9 * 12 * 946 in payments (assuming no PMI) or 102K for owning less stock with no mortgage so in the big scheme of things "not having a mortgage" saves about $6K over nine years or $55/month. (Edited, sorry I had to mess with this ten times to get it right)
You gotta look out for people who argue real estate transactions are as cheap and frictionless as stock market transactions, or insist on weird date ranges in historically bubble economies or rapidly changing demographic economies, or insist tax policy does not exist. Not everything is fundamentally an income stream and you need a plan when a simplification to that fails and you take a massive capital hit. If the error bars on the numbers are large enough, the same number can be interpreted to prove anything. Finally look out for people who confuse average/median with "everyone". All of those are HUGE effects when making financial decisions.
I'm not OP, but I have no mortgage and its worth pointing out that my personal break-even income is obviously twelve times the monthly payment lower than someone with a mortgage, and given a realistic 1/3 of income going to mortgage for most folks, obviously my runway is 1/3 longer than everyone with a mortgage. Also immensely lower stress.