Interest rates affect how much a buyer can pay for a given house, they do not affect whether the house they purchase is a move-up/down house once prices have adjusted for the interest rate movement.
The only time interest rates will affect what a person can buy (as opposed to how much they can spend on a given house) is if those rates are available only to an exclusive group.
It’s just like with the homebuyer tax credit — it affected the PRICES that people were able to pay for a given house; it did NOT mean that they were able to buy “more” house. Why? Because everybody else had access to that same tax credit, which pushed up everybody’s purchasing power. This pushes PRICES up all across the board (though price changes lag as they roll up and down through the tiers), it does not enable people to buy a nicer home.
Given that mortgage rates are at/near all-time lows, what happens when they double and go back to more “normal” levels?
Incentives that are broadly available benefit sellers, not buyers.
