I think it's been tried and what you get is Tokyo. I wouldn't say dystopian but it's also one of the most expensive cities in the world. Apparently the average apartment is about $2000/month.

That's the average price for a two bedroom apartment. You can easily find much cheaper options, the average one room apartment in Adachi ward is nearly a quarter of that.

Edit: Just for comparison, the average two bedroom in San Francisco is $3500, and that's down $1000 from last year

Tokyo is very big. If the only apartments you can find are that expensive then you either want to live in a certain ward or you aren't looking hard enough.

I said it's the average price, obviously about half are cheaper.

If the price will bear it that means people want to live there more than elsewhere. Don't impose your idea of dystopia on other people.