We can solve homelessness, lower rents, and enable people to easily move where they can get jobs or have family. As linked to in previous posts, building more housing immensely helps with that.
As discussed in a previous post, Paris has twice the population density of New York City, but they do it with mostly five story and below buildings:
So your argument about giant skyscrapers is false, because New York City can build the housing it needs without them and with just five story and below buildings like the ones above.
And both people in New York City and the people moving there generally support greater density as posted in a previous post, so we should give them what they want.
It should be noted that I've been talking about things like five story buildings and duplexes, yet you bring up skyscrapers when I never mentioned them. Not sure why you are doing this.