What you quoted is about people taking the only housing they can afford. Keep in mind low income households are 44% of the US. 44% of the country can only afford the cheapest rent. When half of the country has a flat limit, it restricts rent prices, which is why in most of the US there are two grades of rent: 1) cheap rent, which isn't great or 2) slightly more expensive rent where you get seemingly double for it, eg your commute is reduced by an hour, you get all of these amenities like heating and AC, you get way more square feet and so on. For most of the country the difference is around $200 a month.

I know there are wealthier areas like out here in the SF/Bay Area, where there is much more of a gradient due to the average person making six digits. Keep in mind if the bay area was its own country it would be the second wealthiest country in the world, so yes the US has exceptions, but lower income rent is still capped to their income.

If you think housing is elastic either you misunderstand the word or you can always prove it by living out of your car. In comparison, eating out is elastic, despite it being food. You can easily prove it by cooking at home. Maybe you're saying living in an expensive place is elastic so the free market works? Yes, this is true for the upper half of the country. For the lower half it is absolutely inelastic. A tv is elastic, because you can easily prove it by not owning one. Utilities, eating cheap food at home, and housing are inelastic. Try living without power.