I bought 3 houses all for under $20k each over the past 2 years. I use them all as rental houses. You can get waaay under $200k. The problem when you bring this up to people online is they say, "well I would never want to live there". So they are very happy to tell people that already live somewhere that they can move if they don't want new large housing complexes built, but if you tell them that they can move to somewhere more affordable, they act like you are attacking their human rights.
It's triply confounded by the huge group of people who simply don't understand the math behind renting (and this includes many landlords, sadly).
And unless you have literally infinite incoming new residents or people who want to squat on unrented property, increasing the top-end supply will also increase other ranges. It might still not allow someone on minimum wage to live there, but the total number of units increases - unless you replace cheaper units with more expensive same or less density units.
Can't you say the same for people trying to move in? There's plenty of places in the US that you can still get a house for under 200k.