We've gone over this ground before (not surprising in a 965 page thread) and I even wrote some of the posts. But you're right, the history is terrible. Since the 1920s this is the sum total of new stadiums/arenas built in the city, not including onsite rebuilds or land swaps across the street (ie new YS and Citi):
1964 Shea
1968 MSG 4
2012 Barclays
Maybe add Lincoln Center in 1969 which is not sports but did raze a few square blocks for a new performance center. That's it, over nearly a full century. Shea happened because the city had just chased away 2 teams in what was then the country's biggest team sport. MSG 4 led to massive new land use restrictions, including but not limited to Landmark laws, that made everything harder going forward. Barclays took several years on a core location that was undeveloped for decades, had the full support of the Mayor, and still to be massively scaled back.
But with all that, I think it is fair to think this is different for 2 reasons: (1) as far as we know NYCFC not only seeks zero subsidies but even expects to spend money for stuff it does not need to placate pols and community groups, and (2) they seem to have found a spot that will not require eminent domain (though I'm not sure a deal with the elevator factory is done yet). Add in a city and real estate market desperate for economic activity coming back from lockdown and I think this has a decent chance of happening.