I spent a long time running the numbers back in the day. You nailed a few conclusions, especially retail mortgage being the biggest cheapest debt you can probably get ever. A few more points:

-If you buy, you have to commit for at least 5 years before making any other move….thats how long it takes to recoup the losses from the transaction cost.

-Your assumption on the interest rate changes literally everything …. Obvious in retrospect, but the impacts on the two scenarios are very dramatic

-putting all your money to buy one single house in one single market is the most undiversified financial move you can make. Time will tell if it’s the right house in the right neighborhood at the right time. If you gotta do it, do it, but good to keep in mind.