There’s more to it than housing density (see below). For instance, there are also differences in public transport to spread the area of viable housing. Anecdotally, high rent cities such as New York or London tend to not do a great job at providing reasonably priced and efficient transport to nearby commuter towns or suburban areas compared to many in central Europe, for instance.
On densities, cities like New York, San Francisco, and Seattle (high rents) are comparable or higher in density than larger European cities with the exception of Paris (and I may have missed another). London, Berlin, or Madrid are noticeably lower than New York or possibly the other two US cities as well.
(Naturally, the city boundaries of somewhere like London include many less-urban areas so this doesn’t quite capture exactly what either of us presumably mean, but it’s loosely demonstrative.)
I think you are mixing units here (km2 vs square mile). According to wikipedia NY density is 11313/km2 which would ranked 18th city in Europe. SF would be 29th with 7194/km2. I would argue that NY public transit is absolutely doing a fine job (cleanliness appart) and it's moving 7.5 million peoples on a weekday (was higher pre-pandemic)
Density is needed for proper public transit and locally accessible services to flourish.
I don't have datasets for European rents. Can you provide an example of a sufficiently large European city where new density led to a _decrease_ in rents _and_ sale prices?
