It's important to remember that the New York primary is very closed. The deadline for changing your registration was something like last November. Anecdotally, a lot of the young people I know that live here are not even registered to vote here, even the ones that have "permanently" moved here and graduated from college, etc.
The deadline to change parties may have been last year, but there is still time for new voters to register for the first time and vote in the primaries. That deadline is March 25.
But, yes, the New York primaries are ultra-closed and the machine candidate usually wins, especially on the Democratic side.