"Benefit" has nothing to do with it. It's not so much "exporting deliberately" as much as "everyone will submit to our principles, and we don't care if they have any objections."
Downstate NY is not trying to export their ideas, they are simply inflicting those ideas on the rest of the state - under threat of severe punishment. They do not see boundaries; they do not recognize any reason for others to not be subject to their rules. It's simply "we're right, and you will comply. Now."
I live in NYC. There is no deliberate attempt to inflict anything on upstate. However, since downstate pays the bills to a large degree, they do get to call the tune in regards to a number of state laws.
There is no real thought to the residents of upstate. Most of the folks in NYC could care less. Upstate is seen as part of the rust belt with un-needed 19th century manufacturing towns with colleges and prisons.
The whole “rural” versus “urban” debate is idiotic. The booming urban centers aren’t even engaged in the debate. When hints of it echo through the noise of the city it’s greeted with a kind of shoulder shrugging bewilderment.