The NYTimes/NerdWallet calculators implicitly account for that in their logic - they track money you gain/lose from down payment/mortgage/interest/taxes, then selling the house at the end.

On the renting side, they only assume investing the money that isn't going to down payment/monthly mortgage payments, not investing the full value of the house.

My blog post here is just giving an argument that 2 of their parameters should be updated, then showing the result of that update.

Usually these kinds of calculations take that into account. E.g. the up front investment in the stock market == the downpayment on the house. But remember that you're paying for that leverage with interest, which further eats into your gains on the house.