Landlords and owners will be able to command high fractions of average incomes as long as there is no slack in the housing market. If you nationalize housing and hold prices low, then there will be supply shortages where some folks will not be able to get housing who would happily pay your price. (This is a fact, not conjecture, and is easily observed in any affordable housing lottery in the United States.)
The only way to have low prices and also to satisfy the demand for housing (i.e. have each person who is willing to pay be allocated a unit) is to have slack in the market. No other solution will do it.