there absolutely should be a profit for rent. Being a good landlord is work, work should be compensated. Taking the risk of ownership (low though it might be) should be compensated.
The issue isn’t profit. The issue is a) artificial lack of supply driving up prices b) greed and exploitation of basic needs.
In some countries, like some of the USA, you get clean drinking water pumped into your house for your toilets. However you do the math a) people need to work on the system to keep it working and they should get paid a living wage b) water is a need even more than housing. We pay for water, and people make profit on it. How you pay for it - taxes, city rates, privately - whatever, you pay for it.
that isn’t the issue, just like paying rent isn’t the issue. it’s the amount which is.
the solution is simple and already exists: universal basic income, and make basic needs like water and rent limited by this amount.