We already tried that. It turns out that people are racist, so now we need laws to protect against that. It sucks for all the decent non-racist folks but the alternative of not having those protections was far worse.
1. I can see this being effective against larger landlord that will have many units available every year, ensuring that adequate testing can be performed. But on smaller landlords with only a few units, it seems like it'd be hard to test. (for example, you get rejected from an apartment. The landlord rents it out to someone else. You file a FHIP complaint, but the landlord no longer has any units available so they cannot test.)
2. It seems like this is largely driven by complaints? If I was rejected from an apartment, I'm not sure how I'm supposed to glean whether or not it was based on race.
Why couldn't the same law apply to residential leasing?
I'd also argue the stakes are higher when leasing, so landlords will be less likely to take a chance on a race they don't like. Most jobs in the US are at-will employment so you can be fired at any time for almost any reason, but evicting a tenant can be a long process.
It is possible to prove a company is disproportionally one or the other when making the claim. Of course when an industry has far less applicants or members of a certain group that's to be expected but still. Consequentially I've heard of some pretty blatant race based selection especially in the US. It's just that that selection ends up excluding white people (or east asians) A while ago I even discussed with a hr person here on hn who was defending their hiring of that sort with the most flowery wording about 'just giving priority' or 'reaching out to members of their prefered group specifically' fist if all they get is not the desired group.
Having a large non-white population is not a protection against race-related discrimination.