With rent control and required payments to tenants for no-cause evictions, we will see more rent increases, more for-cause evictions, bigger deposits, and tougher screening by landlords. 
Rent control doesn't lower the cost of buying, building, and maintaining rental properties. It does not defray the costs to replace carpets, screens, appliances, vinyl, or fixtures, nor does it reimburse the property owner for paint and cleaning after a tenant trashes the property. That will get passed on to future renters.
Yes, rents go up. So do taxes and all costs associated with buying, owning, and maintaining property.