Over half of the for-profit rental stock in the US is owned by people or companies with over 25 units. And they are more than happy to let empty units stay empty if it will keep the value of their other units high.

It's not the "1-2 house landlords" driving prices up.

https://www.pewresearch.org/short-reads/2021/08/02/as-nation...

"Individual investors owned nearly 14.3 million of those properties (71.6%), comprising almost 19.9 million units (41.2%). For-profit businesses of various sorts owned 3.7 million properties, or 18.8%, but their holdings totaled 21.7 million units, or 45% of the total. Entities such as housing cooperative organizations and nonprofits owned smaller shares of the total."