Address what? A vague reference to "stickiness and inelasticity when it comes to housing?" I suspect you're misunderstanding what the "swap houses" example means. It's not actually about two people who might want to swap their houses. It's just a "bottom up" way of showing how housing restrictions create inefficiencies by limiting choice.
It might help to think of it in a "top down" fashion. Imagine laying out housing for everyone in a metro area as an optimization problem, where you're trying to maximize a value function over things like amount of space, proximate to peoples' workplaces, quality of schools, affordability, etc.
Housing restrictions add additional constraints that make the solutions worse for everyone. E.g. say some group of people with kids are willing to live in a duplex on 1/8 of an acre rather than a detached home on 1/4 of an acre in order to reduce their commutes and see their kids more often. But they're not willing to live in a city apartment with their kids and pets. Housing restrictions basically eliminate that part of the solution space by making it illegal to construct such housing. That group of people get punted to their less-preferred alternatives, and the resulting solutions are worse for everyone.
It might help to think of it in a "top down" fashion. Imagine laying out housing for everyone in a metro area as an optimization problem, where you're trying to maximize a value function over things like amount of space, proximate to peoples' workplaces, quality of schools, affordability, etc.
Housing restrictions add additional constraints that make the solutions worse for everyone. E.g. say some group of people with kids are willing to live in a duplex on 1/8 of an acre rather than a detached home on 1/4 of an acre in order to reduce their commutes and see their kids more often. But they're not willing to live in a city apartment with their kids and pets. Housing restrictions basically eliminate that part of the solution space by making it illegal to construct such housing. That group of people get punted to their less-preferred alternatives, and the resulting solutions are worse for everyone.