Technically, for many owners their carrying costs do increase year over year. Property taxes, HOA, maintenance, etc all tend to increase over time. Depending on where you live, these non-mortgage costs can be thousands of dollars per month and they don't go away when the mortgage is paid off.
If you look at it in terms of portfolio construction, you would never want more than 10-20% of your net worth in your home, much less the 50+% many people have in practice. Owning your home is a pretty mixed bag, financially, and made worse in practice because people have far too much of their net worth in it. They'd benefit from renting much longer and buying much less home if it was a financial argument.
I've owned my current home for several years, and go back and forth between renting and owning. Even though I live in a "hot" property market and benefited from appreciation, I actually lost money versus renting the equivalent and investing the difference, and I do keep track.
Carrying costs are important to this consideration. They shouldn't be significant compared to rent or the payment, but in some areas they are.
I fully agree that 50% of net worth in a home is too much. Though I doubt that the people you are thinking of actually have that much net worth in a house - the house might be worth that much, but odds are they only own 5-10% of it, and the rest is net worth of the bank. By the time your house is 50% yours you should have seen enough decrease in carrying costs - compared to inflation - that you have more investments elsewhere to pay it off.
The analysis of lost money vs investing needs to compared over a lifetime not a shorter span. Your payoff comes at the end when you need much less invested in the first place to pay for the rent you no longer owe at all. If God hasn't told you the future in detail you can't know: how much will inflation be, when will you die, and other such things that affect how your lifetime investments play out.
That last also gets into life goals. if your plan is to live cheap and work for the rest of your life to leave a large sum of money to your heirs that means a different investment strategy vs someone who wants to retire early and leave nothing behind when they die. For the latter there is a difference between someone who wants to retire and spend all their time in the shop building something vs someone who wants to retire and travel the world.
Only you know your life goals today (and you don't know how they might change in the future!) so you need to make the right decisions for your. Renting and buying a dwelling both have pros and cons so there is no right decision for everyone.
If you look at it in terms of portfolio construction, you would never want more than 10-20% of your net worth in your home, much less the 50+% many people have in practice. Owning your home is a pretty mixed bag, financially, and made worse in practice because people have far too much of their net worth in it. They'd benefit from renting much longer and buying much less home if it was a financial argument.
I've owned my current home for several years, and go back and forth between renting and owning. Even though I live in a "hot" property market and benefited from appreciation, I actually lost money versus renting the equivalent and investing the difference, and I do keep track.