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They did this in New Zealand under Jacinda Ardern's government and house prices have started to fall, but only slightly so far. IIRC the rules were something like, lots in a certain radius of a train station or town center are mandatory mixed-use zoning, overriding any city rules to the contrary. It was very controversial for the national government to override city governments like that.
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> In several opinion polls, Ardern's domestic popularity had reached all-time lows by 19 January 2023...[when] Ardern announced she would resign as Labour leader and prime minister by 7 February. -Wikipedia

Other political leaders might hesitate to follow such footsteps.

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i think making it more restrictive would be better?

"affordable housing" is the same thing as "luxury housing" asides from the rent

sure, you could allow less restrictive builds so that you only get a room with no bathroom or kitchen for $4k but thats not actually better

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That's not how it works. More competition will bring the price of those down.
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