It isn't quite as simple as that in many cases. Kickbacks from brokers and other dubious jiggery-pokery can make quite a difference.

Doesn’t it stand to reason that without broker fees the landlord margins would increase bringing more landlords (supply) into the market?

That's like saying rent prices depend on the will of god. Retroactively, you can justify this claim regardless of what happened: "It was god's will" or "You had to adapt your price to the demand".