Lots of people have considered this.
How big a concern it should be depends on how tight your budget is, and details of your desired housing, including what current prices are. Roughly, it should be of little concern if you have substantial slack, moderate concern if you have little slack, and great concern if your budget is stretched to the limit but you are also very determined to live in an area with high but currently rising rental prices.
My personal opinion is if your concerns are general, you should narrow them down somewhat, because preparing for All Possible Concerns is expensive. If your concerns are specific, you should examine them more directly, perhaps with a case study.
Re rent specifically, rising rents usually are coupled with housing prices that are higher than the rents. So renting is still cheaper in expensive cities. It often happens that you can barely afford rent in a costly city, but you could buy a house in a cheap one.
As a grand generality, my first exposure to to real estate prices came in a "philosophy/literature" book we read in high school English called "On Walden Pond." Home Slice Henry David Thoreau built a cheap cabin by a pond outside of town in 1840s New England (I think Massachusetts) and grandly lived there outside the normal realm of getting and spending, then wrote a book sharing his thoughts about the matter. He didn't include the part about visiting Mom's house for meals sometimes when he was hungry, I'm told. The part I remember was him saying that people usually spent about a third of their income on their house.
Rent details may vary from era to era, but today, ordinary people still spend easily a third on housing. I assume prices can vary by thousands of dollars per year, but not infinitely. Plan for moderate variances.
PS. It's always possible to respond to rent increases with "badassity", in the form of some thrifty behavior change - move, find a work-for-reduced-rent deal, pack in extra roommates, earn more, shift to a custom van, fix up a fixer upper and fill with renters, or other. Flexible badassity is the point of MMM.
"Always" here means "unless you have already found the best possible rent situation, and you have left yourself such a tight budget that's the only thing you can afford." IMHO, FI means leaving yourself more flexibility than that.