I really like the interactive graphs but I can't see how you're accounting for the cost/value of the use of the property. The return on investment for paying rent for 30 years is exactly $0.
I think what you're really comparing is if the stock market or the housing market is a better investment, but you're not taking into account that the use of the property has value.
Think of it like a landlord, you're not just investing in a house to let it sit empty and then sell it later, you're buying it with the intention of collecting rent every month. Or to put it another way, it's like comparing the prices of dividend and non-dividend stocks without accounting for the dividend.
For a personal home, you need to account for the fact that owning it means you live there rent free. There's a monthly cost for the mortgage, but that cost doesn't increase with inflation the way rent does. Owning a home comes with expenses for upkeep and taxes, but once the mortgage is paid off those are the only thing you have to account for.
> I can't see how you're accounting for the cost/value of the use of the property
That's what the rent/buy calculators are doing! It's summing up all the cash flows for owning a property (down payment, mortgage, taxes, maintenance, etc, and then crucially selling it after 30 or so years) and for renting a property (rent, and investment income from money that would have otherwise went to down payment/mortgage), and telling you how the results differ.
All I'm doing is tweaking 2 of the parameters of these calculators: The rate the home appreciates in value, and the rate cash investments appreciate in value. Everything else stays the same.