I'd have to say then that Syracuse is just a very unique school. A friend of mine graduated and it seemed his entire social circle moved to NYC for jobs. I wouldn't say it has a national following, but being a large wealthy private school, it has more of a national following than other state schools. Reminds me a little of USC and Miami. And I would still bet it has a larger following in the state of NY than any other school in the state. Of course, I could be wrong.
And yes, Syracuse does have that PR branch known as espn.
I agree on your first point, disagree on the second.
NY is so fragmented for sports. WNY is U Buffalo. Central NY and Capital Region are Syracuse.
There have been studies over the years that show Notre Dame and PSU are most popular in NYC for football. Then there was that dumb google search metric by 538 that showed Rutgers. Tranghese said it's UConn and Syracuse for basketball.
In other words, NYC is an absolute wash with many many schools competing and none rising above 20% in market share in a city that doesn't care a whole lot about college sports.
As for social circles, academics, and NYC for jobs, it's such a big state with so many great schools, most of them private, like Cornell, Columbia, NYU, etc., that it's hard to make the case that Syracuse is dominant in the mindset. It's not.
The mindset of most kids in this state targets the SUNY centers and Geneseo for affordability, and then NYU as a feasible school if they can afford it. The lure of leaving either NYC or anyplace upstate and west for Syracuse (and private tuition) is not that appealing. Given the choice, schools like NYU or even U Rochester win that debate.