Given that each city effectively has unlimited housing potential, the idea that tourists are driving out locals makes zero sense.
Construction does not fix the fact that tourists pay 5-10x what local residents do for the same real estate. If you want to keep that from affecting rents, there's a very effective and inexpensive way to do it: don't let people turn rentals into hotels. Just like New York.
I mean if you're willing to take the subway to work, you can get a pretty large 2BR for less than $2K / mo. Yes you need a job to be able to afford that, but not a particularly amazing job. Just not unemployed for the entire year every year.
https://streeteasy.com/for-rent/nyc/price:-2000%7Cbeds:2?vie...
Density increases innovation. Density decreases travel carbon emissions.
A city of skyscrapers would also make a pretty dystopian city, the way I see it.