At some point you need to realize that the middle class is also geographically gated.
There's a reason why the classical middle class picture is a nuclear family in the burbs and not on 5th avenue.
The American middle class was never "rich" it was very financially prudent. If you still willing to live in the burbs 250K in NYC will get you a very nice house, a car and even college tuition for your kids.
Even in the golden age of the American middle class there were plenty of areas that were out of their reach, thats why the middle class expanded into new sub-urban developments. The cities were mostly polarized as they housed both the very rich and the very poor.
I agree with you but the NYC tri-state area is a strange place and not a great example for the stratification effect. You're worse off in the NYC burbs in in many cases, one would think it would be the opposite but it's not. The amount of money it takes to break out of the middle class quality of life is more around 400k per year for the NYC tri-state area. In the burbs the houses are not nice or good for the price, they're overpriced and property taxes are outrageous- property taxes can actually be worse in the suburbs than they are for a Manhattan condo or coop. The commute is also a killer, while Metro North is somewhat reliable and on-time relative to other rail systems, the length of the commute is just brutal. At least while you're paying more per square foot in NYC you do get some convenience out of it, although this gets more complicated if you have kids. If you've got to worry about education for children, you MUST buy a coop/condo in a NYC district with good zoned schools, this isn't common and those district command the highest prices per square foot. If you can't afford those districts your looking at private school for the kids, and that runs 30-40k, somewhat less if you choose a Catholic school but still a huge chunk of your budget. Trust me, there are places you don't want your kids going to public school- and I'm not talking safety, this is in regards to the piss-poor quality of the education. You'd be better off home schooling in some places. The burbs do have better schools overall, but you're still stuck living a middle class lifestyle with a soul-sucking commute in the NYC burbs on 250k.