Everyone wants their city to remain the same as it was when they moved there, and unfortunately they have the political power to obstruct new construction.
Even in a no-zoning "paradise" like Houston, short-term economics rule the roost. Approximate rule of thumb in the US I've heard is if a Single Family Residence is 1X cost per unit living area, a Multi-Family Residence (about 3-4 stories) is 3X, and a high-rise is 6X. Developers turn over inventory way faster at the 1X multiplier by selling to a bigger market. This is also confounded by American expectations of living space; they're not tempered much if at all by moving into apartments and high-rises, so costs go up.
US residential growth planning is all kinds of dumpster fire ugly, so these are by far not the only factors that contribute to why we don't see more high-rise developments in American cities. Just the tip of the seriously messed-up iceberg.
That's probably not true, although it depends where you are comparing it to.