Mortgage: 100,000$
Term: 25 yrs
Rate: 1%
Principal payment for the 12th month: 59.38$
Interest payment for the 12th month: 993.84$
Cumulative interest after 12 months: 11,998.64$
Cumulative principal after 12 months: 675.02$
All this with an incredible 1% rate.
Storing any amount of money for the amount spent is better than banking none of that money.
Honestly I downvoted your earlier comment specifically because of your edit saying that it doesn't matter if equity is 900/1000 or 10/1000. It matters a hell of a lot. Only a fool* would avoid putting 900/1000 into equity, with an effective 'rent' price of 100 if they move out after a few years. But there are real decisions to be made if just about none goes to equity.
*assuming they expect to live in one place for a while
Of course when you are down to a 1% storage of wealth other investments become much more attractive. You could rent the equivalent house (assuming price is the same) and be confident that you could make up the difference by investing what you would spend in transaction fees etc.
It doesn't take much improvement in that storage rate, though, for that confidence to evaporate.
It's not just the cash flow which matters, you must consider many other factors. Have you heard of "depreciation", you know the expenses required in order for your house to keep its value? It's a whole lot more than the "10$" gained in the first years when using a mortgage. You keep focusing only on the cash flow of one part (mortgage vs rent) of the whole deal and ignore everything else. That's nonsense.
And because you "simply" forgot to include maintenance and property taxes, you end up being just plain wrong. In reality, a house is a money pit in the first years of the mortgage. Whereas in your simplified example it looks to be a good deal because it's assumed one is gaining $10K in equity every year.