While not based strictly off population, the US Census Bureau’s statistical areas seem to align well with common usage of the place=city tag in OSM - an important regional hub. Statistical areas were used for identifying regional centers in New Mexico’s highway=trunk network using this guidance: “a city is considered the urban core of any Metropolitan Statistical Area (MSA) or Micropolitan Statistical Area (μSA) that is not part of a Combined Statistical Area (CSA) that contains a MSA. If the μSA in question is part of a CSA that does not contain a MSA, then the largest μSA in that CSA shall be considered a city. “ Most cities in New Mexico follow these criteria. The two exceptions - Deming and Grants - are towns of about 10,000 people located within a commutable distance to a much larger metropolitan area. A little more under the radar, when someone decided to tag every incorporated place in Wyoming as place=city, I used these same guidelines to clean that up, leaving only the Census’ statistical areas as cities.

For New York, it might make sense to only consider metropolitan areas as cities. That would align with your threshold of 50,000 inhabitants, except that is not restricted to the city limits but instead the entire statistical area for a metropolitan statistical area. This would result in places like Binghamton, Ithaca, and Watertown retaining their city status while preventing places like Clay, a suburb of Syracuse with just over 50,000 inhabitants, from getting tagged as cities.

With that said, I think this mechanical edit will be a big improvement overall, and the cities will be easy to clean up after the fact.