The correct solution to this problem is to tax the rental income and hand that money to low income households. It would create a balance of correct market prices and allowing low income people to stay.

Just letting the price float and pushing low income people out creates an unbalanced society where a class divide builds up over time. Modern housing policy in the UK is to mix social housing with regular housing developments, having social housing all grouped into one location was a catastrophically bad idea from the post war era.