I personally agree with the idea of full-height platform screen doors being installed in New York.
Yes, it will require standardised train lengths as well as precise stopping. It wouldn't be easy to stop exactly at the point where the train doors match the screen doors.
However, screen doors can prevent people from jumping onto the rails and thus allowing for smooth train traffic without much disruptions from these fatal incidents.
Platform screen doors are expensive to maintain. The screen doors require manpower to regularly clean it as it collects dust all the time. If any of the screen doors shatter, it will cost quite a huge sum of money to replace them.
Overall, I think the idea of platform screen doors is great for a long run, especially for subways with long networks of underground lines. You may choose half-height platform screen doors for elevated and at-grade stations, these are used in Sunny Bay station in Hong Kong as well as quite a number of elevated stations in Singapore.

Platform Screen Doors at CC6 Stadium on the Circle Line [Underground].

Half-Height Platform Screen Doors at EW26 Lakeside on the East West Line [Elevated].