When interest rates fall the value of the asset goes up and the cost of borrowing the same amount of money has gone down
Firstly, people can afford to pay $x for mortgage interest. The "cost" of borrowing remains constant because incomes don't change. As mortgage interest rates decrease, $x doesn't change. Instead people can borrow more (for the same amount spent on interest) and they bid more. So house prices go up.
Okay, on rereading: one problem is that I have never heard of "buying down" because I think the concept doesn't exist in the New Zealand market. The US market for mortgages is extremely different from most countries. I wrote my comments generic enough to cover both (I hoped).
Buying down is not a neutral option: I presume it is making a bet on the future of interest rates. So I'm not sure your logic follows. If we want to make interest rate bets then there's lots of different worms we can eat.
The information gap remains!
Only in a perfectly spherical house market. In my limited experience (non-US market), your assumptions are poor. Opinion:
1: You often can't get a mortgage on the same terms so you often can't find equality between selling a home and buying a home.
2: When the market is down, turnover can reduce drastically so your choices for a house can be severely restricted.
3: when the market is down, prices are sometimes driven by unwilling sellers and bargain hunters. A desirable home may sell at a reasonable price but an average home might not.
The market is often down when interest rates are up and you can't get a mortgage on terms that suit you.
> You're born "short housing"
You are short the "minimum" necessary which is a lot smaller than a whole house. You are not short 1.0 houses. Maybe short 1.0 rooms. And it really depends on who else you are tightly linked with (family or partner).