In e.g. San Francisco, more than half of the city is zoned to only allow detached height-limited single-family houses or sometimes duplexes, with businesses restricted to designated commercial streets. When you add wide streets with several wide lanes, generous street parking, parking requirements for buildings, long skinny land parcels with (often unused) space for a small yard in the back, etc., land use overall is incredibly inefficient even if you want to preserve the “local character” of low buildings.
Look at the sea of light yellow zones in the zoning map, http://default.sfplanning.org/zoning/zoning_map.pdf
And among cities in the region SF has higher density and more flexible zoning than most.
If we upzoned the Richmond, Sunset, and Marina neighborhoods from pale yellow to orange and purple, and added better transit, we could easily double the population of the city without anything taller than low-rise apartments.