Rising rent isn't necessarily a major issue. Given apples to apples comparison, (Person A/B have identical incomes, savings pools, and acquire identical homes, but A rents and B ows), the compounding on the now-invested downpayment plus added savings from lower costs should exceed rent hikes. People tend to point out the costs of rent, but ignore the opportunity costs of ownership. 

Yes, rent should cover costs, but remember that the average apartment's a lot better capitalized than your typical new home buyer meaning far lower carrying costs. If the unit's paid off, the landlord's operating costs are minimal and he's massively profitable at rents that would cripple the new entrant, who can certainly try to recover costs but may not find themselves able to due to market conditions.