Portland, OR solved that problem by making landlords accept the first offer which matches the stated requirements. Which leads to some… interesting incentives :p
Seattle has this also. It leads to very stringent requirements, with little room for flexibility, you also have to the first qualified person to respond to an ad. It has also led to a lot of rental supply not being advertised, relying on personal connections to find tenants instead.
It's also difficult to nail landlords on, so it goes largely unenforced (at least in Seattle). Most renters aren't going to be able to afford to take a landlord to court over an apartment they didn't get, they're just going to keep hunting because they're usually on a strict timeframe to move.
Most landlords are sophisticated enough to follow the rules, but it does affect corporate landlords (who always advertise and whose employees can lose their jobs if they don't follow the rules) more than private ones.
