It really depends on the landlord. I just renewed my lease on a single-family home in a relatively hot market with no price increase. Of the 7 or 8 different units I've rented across 4 different states, only 2 of them had landlords that routinely nudged the rent upward at lease renewal. My personal experience is that unless someone is really working to maximize profit per unit, they're usually content to leave well enough alone, and only raise rates when the unit goes empty. I know multiple people who've rented for 15+ years with no increase in rent.
Indexes and aggregations may show something, but it's important to remember that they're lossier than many people appreciate. You'd have to dig into the data to learn how representative it may or may not be. Since small-time landlords are hard to collect data from, most of these city rental indexes are probably relying on large-scale apartment landlords who are constantly trying to squeeze maximum price-per-unit. I'd say you'd do well to take it with a grain of salt.