There are plenty of housing units in the USA. Housing is extremely affordable in parts of many major American cities such as Detroit and Baltimore to name just a couple. For example you can buy a house in lovely Baltimore for under $25,000 in a neighborhood with amenities like a walkable park, and tennis and basketball courts[1]. The complaint is never really "housing isn't affordable," it's more along the lines of "I can't afford to live in the most desirable coastal real estate in the entire world" or "I can't afford to live in a safe place with a good school district" (a classism/racism dog whistle if ever there was one).

[1] https://livebaltimore.com/neighborhoods/madison-eastend/