The flip side is, do ownership costs go up as quickly as rents? Depends on your market obviously.
I'm not disputing that you should get out of rental properties in retirement, but in Berkeley, our landlord was sitting on units purchased by his parents in the 1960s. He was allowed to raise rent to market value when a tenant left, which meant that when we left, we were paying $700/mo and all of our neighbors were paying $1200 to $1400/month.
For a building with no mortgage and minimal upkeep costs, $20,000/month was a nice retirement income for our landlord. I would guess today, based on friends who still rent in Berkeley, that building is bringing in $30,000/mo.
But of course, he wasn't "free" like he would be with an annuity or something like that. Always headache, finding renters, dealing with problems, damage, etc, etc, etc.
In fact, I thought he would be itching to get rid of us and pull in an extra $700/mo. When we left, he was so sad - he said having me work from home was like having free on-site management and he worried a lot less than he had in the past and now would have to worry more again.