Paris is one of the densest city in the world (overall, there are denser areas) despite having a cap at 6 floors on building height. (I might be off by a floor or so) At that height the cheapest building technologies* still apply and up is not that expensive.
Now going up to 200 floors is very expensive. However on a per unit area it is only a few times what the cheapest building style* is. So it does require more expensive rent, but not that much more expensive, and as rent gets expensive you expect apartment sizes to fall to balance some of it out.
* cheapest that can meet reasonable building codes. I'm ignoring the uninsulated, fire-prone shacks you see in poor countries which are cheaper by far.