Let's use 4 plexs instead of chicken.

You have a vacant lot. You can build a house, house with an ADU to operate as a rental, or a 4 plex (live in 1, rent 3). If you can't charge rent that covers your costs, building the rental isn't worth it. You would be better off putting your extra money in the stock market or building a nicer house for yourself and building equity that way. Note that putting money in the stock market gives corporations more power.

Getting back to chicken... If farmers had a cap on how much they can charge for chickens, they would stop raising chickens if the price of feed went up more than the cost they are allowed to charge. If restaurants had a cap on what they can charge for meals, people wouldn't open restaurants if they were at risk of having to pay more to run the business than what the business earns.

Most people aren't hording apartments. Lots of middle class people have a rental or two. If you want 4 plex building to add to the missing middle housing, it needs to be a worthwhile 8nvestment. If you squeeze out middle class property owners, you will be left with corporations only.