“If we can find a bunch of billionaires around the world to move here, that would be a godsend,” Mayor Michael R. Bloomberg said somewhat peevishly when the buildings — none yet completed, some yet to break ground — had become a political football in the campaign for his successor. “Because that’s where the revenue comes to take care of everybody else.”

That is, unless those billionaires don’t actually live here: Buyers parking fortunes in places like One57, across from Carnegie Hall — where two penthouses reportedly sold for more than $90 million apiece — often keep their primary residences elsewhere, as James B. Stewart noted recently in The New York Times. So they pay no city income tax, and in these new luxury buildings, property taxes are comparatively low — “even,” the column pointed out “as the city’s services prop up the value of their trophy real estate.”

One57, is Exhibit A in what we should be able to prevent. Developed by Extell, this 90-story apartment tower made headlines last year when a crane nearly fell down as Hurricane Sandy approached. Its French architect, Christian de Portzamparc, won the Pritzker Prize 19 years ago and during the late 1990s designed the compact LVMH Tower up the street, a jewel-like building.

This one unravels as a cascade of clunky curves descending toward ribbons billowing into canopies. The conceit is falling water. The effect: a heap of volumes, not liquid but stolid, chintzily embellished, clad in acres of eye-shadow-blue glass offset by a pox of tinted panes, like age spots. It’s anybody’s guess how the building got past the drawing board. It is now enmeshed in an anticorruption investigation, centered around a tax abatement that Albany legislators tucked into a real estate bill in January.

Extell is also the company that put up the two towers on Broadway at 99th Street that caused so much tsuris on the Upper West Side that new zoning regulations were cooked up to stop construction of more high-rises in the neighborhood, effectively guaranteeing the views from Extell’s buildings.