Large scale landlords and would be tenants are both pretty familiar with the market. The only people not familiar with the market are mom and pop landlords who tend to not update rent with changing market conditions. This increased transparency might cause them to raise rents because it'd be easier to do comps, and they wouldn't previously undercharging a tenant to make it harder to find a new tenant at a higher price.
Some mom and pop landlords (including myself) prioritize for having sustainable, enjoyable tenants. The gold standard is a tenant who requires little upkeep, pays on time, and stays for a long time. I won't increase the rent on tenants who are easy to work with.
If a new prospective tenant asked why the price is going up, I'd explain that it's the going market rate, and they're welcome to find another place. I doubt transparency would change anything when listing prices are already public and rarely negotiable
If one was looking for such a landlord, what should they be looking for on the listing? Is there a common place where you might choose to list a rental that's not as frequently used by big players?
Ask your friends and extended family about it. Especially if you're looking for single bedroom apartment. You never know, X's grandfather can have a small appartement he doesn't want to put on the market because it's a hassle, or your cousins' family (the other one) can have the perfect appartement for 2 people, 2 minutes from the sea, 5 from the train station, and you just have to wait a year for it.