The zoning described was actually quite generous by modern standards; you could technically build as much as you wanted as long as it fit the prescribed cake tier shape, and you could build theoretically unlimited height on a certain portion, I believe the center quarter of the lot. There is no city in the US today where you could build something as tall as the Empire State Building as of right; and yet the older regulations allowed that.
I'm not sure what you mean by that. 6 buildings taller than the ESB have been completed in NYC since 2014, mostly residential towers of the sort described in the OP.
https://en.wikipedia.org/wiki/List_of_tallest_buildings_in_N...
Nearly all tall buildings in New York these days are legally built through assembling "air rights." Zoning has predetermined height/FAR limits for all lots, but in certain areas it is possible to sell currently unused rights and transfer them to the owner of another lot. This allows some developers to build taller but keeps overall neighborhood square footage around a prescribed limit. This way, you can build a spiky tower or two here and there on Billionaire's Row (the general name for the area) but the street cannot become a wall of them.
More info on air rights: https://streeteasy.com/blog/what-are-nyc-air-rights-all-abou...
But these days in most American cities there is surprisingly little you can actually do with your property without subjecting yourself to additional review or exceptions.
Some amount of community review is good at a base level, but the gone wrong example YIMBY activists likes to trot out is the ridiculous example of San Francisco's "historic laundromat" saga. https://missionlocal.org/2018/06/the-strange-and-terrible-sa...
Even once a building is built, zoning legally constricts what you can do inside it. Most residential developments do not allow operating small businesses from the home (you can't be a hairdresser in your own house). I'm not sure how exactly this will play out once the pandemic is over and nosy neighbors start poking around at who's WFH. In fact this already happened to a Seattle cidery: https://www.seattlepi.com/lifestyle/food/article/yonder-cide...
NYC created the world's first zoning laws in response to a building casting shadows: https://www1.nyc.gov/site/planning/zoning/background.page