It's really worth highlighting that in most of the US it is illegal to build anything other than single-family homes ("SFHs"). The sort of medium density neighbourhoods a lot of people like are an historical anachronism in zoning terms.
It's true there are local issues too. For example, New York's scaffolding laws just make all construction expensive [1]. Basically any gravity-induced incident is 100% the employer's fault and this hugely drives up insurance costs.
Tax laws play a part too. Ultra-luxury apartments in NYC not only don't pay their fair share of property tax (in terms of market value), which is an issue New York State has to fix and has refused to for decades because upstate SFH owners don't want to pay more tax (SFHs in NY pay way less property tax than an equivalent value apartment). Ultra-luxury getting property tax abatements for new construction is a crime.
But here's a key general issue that has been proven true around tdhe world: anywhere with the free flow of capital such that you can park money in real estate in the world's urban centers with little to no oversight have experienced huge increases in property value. This incentivizes ultra-luxury pdroperty development. We need to stop this.
We need:
1. More multi-family building in SFH zoned areas. Areas that prohibit this should be penalized for it with higher property taxes (if it's not outlawed entirely);
2. More medium-density development along transport corridors where we can and do create walkable neighbourhoods; and
3. More high-density affordable housing in urban centers.
[1]: https://www.nytimes.com/2013/12/18/nyregion/campaign-underwa...