If there's 150,000 identical homes for rent in an area, and 200,000 people/couples/families want to live there, then 50,000 are going to be shit out of luck.
The going rate is going to be the maximum that the 150,000th person out of those 200k is prepared to pay.
How do you fight maths?
Build more houses. Less competition means lower prices.
Social housing schemes.
Work from home being a right so you don't end up with everyone needing to work in a massive city to make ends meet.
Tax landlords. They're already charging the most the market will bear, and taxes would mean they can't just snap all those homes up and offer them for rent. If buying and renting homes is a valid business plan, then the tax isn't high enough.
The problem is there aren't 150,000 homes for 200,000 people. It's probably the double but 100,000 of those homes are owned by people/companies who'd rather have them empty while the price rises. Basically using them as stocks instead of shelter for actual persons.