The last few cities I've lived in have seen 10+ straight years of rent increases (with a brief drop then rapid spike again from COVID) so... they do already do this?
Writing in the context of preceding comment. Landlords increase prices as much as they're able, they don't decline to increase when they could to maintain some fixed margin. I'm not saying they're generally unable to rise prices in general, but that they have no special additional capacity to raise prices in response to land taxes.