They are the market. Who else sets prices other than landlords? How can a "rent is too high" issue not be a landlord issue?

It's a greed issue. "They get x amount so I should too." Then someone decides it's a new year so the prices go up and the same thing happens (now accelerated by algorithms that grab data about market prices) and the landlords look around again and say "they're getting more so I should too, it would be stupid for me not to!"

Who else sets the prices for them to be too high in the first place if not landlords?

My uneducated solution is price caps based on some calculation of a typical income for the local area (NOT a family income, we don't need more of this "2 people are required" bullshit.) If that means some people that could afford more are getting cheap rent I don't care as long as it means the typical Joe who can't afford to buy has options that don't leave them perpetually unable to save. If that leaves some people unmotivated to rent that's fine too, in my experience there are plenty of homeowners who want/need to rent their basement/garage/etc to cover their expenses.