Taxing the extremely wealthy basically does nothing to decrease the property values of this class of people en masse, and decreasing their property values en masse is precisely what it would mean to make housing more affordable for more people.
"But CHILDREN will SCREAM here!" shouted one such lady at me when I dared express my opposition against her petition, which demanded a stop to a "megalomaniac" plan to build approximately fifteen apartments half a kilometer away.
"You were a child once, too," I said.
"Sure, but I was A GOOD BEHAVED ONE, NOT LIKE TODAY'S BRATS!" at that time, she was positively screaming as well.
M'kay.
The situation in the US may be different, but the few YIMBY blogs and articles I have read mostly described their efforts as an uphill battle against progressive politicians who were certain that development leads to gentrification and gentrification is bad. Given that the YIMBY movement originated in California, this may just be an aftereffect of Californian politics. But in general, it is blue cities and regions that are known for very restrictive zoning policies.