Lou, let me preface my remarks by saying I cannot answer all you're asking. However, in regard to why some players are able to achieve this distinction, and are viewed in that respect, there are a few key ingredients that seem to typify that kind of player.
Now, again, I am thinking in terms of a player to a city, not so much nationwide.
He seems to be someone with the same club for 8-10 years, or more.
He seems to achieve strong stats, leading his team, and is often at the top, or near the top, of the league leaders.
In clutch situations, he seems to come through the majority of the time.
He seems to be quiet, and yet affable to the press. The camera likes him, a phrase I got from the immortal directer, John Huston. Thus, he seems to give decent interviews for the papers, and proves even better in front of the camera. Athletes, when you boil it all away, are indeed entertainers. So, the combination of sport performance, especially when you "rise to the occasion", being a good interview, and finally, if you are genuinely friendly and wholesome with your fans. Of the latter, hockey players used to be among the very best with their fans. The legendary Maurice Richard, the recently deceased Gordie Howe, and Bobby Hull were adored by their legions of fans, and the feelings of love and respect were reciprocated by these three gentlemen right back to their fans. Their fan-hero relationship was priceless.
Some athletes believe the only thing they owe the fans is their best performance, and then leave me alone. I do not want to be bothered by you. Get away from me---you make me nervous. Whatever. In time, they've assassinated or bludgeoned enough of their fans emotionally, that people look at them at best as a mixed bag.
When Rocket Richard died, all Montreal went into mourning. I suspect the same will happen in Detroit with Gordie Howe's passing. Or when the time comes that Al Kaline leaves us. I sure felt that when Ernie Banks passed away, as he was my hero growing up in the suburbs of Chicago in the 60s.
I wasn't from New York, but it hurt when Mickey Mantle passed away. I was in anguish.
Summarizing, you gotta be good, be good in the clutch, and be friendly with the press and with your fans. They make you.
Or else, they wad you up like a piece of waste paper and spit on you if you ignore them, are mean to them, or hurt them or their child!
Just my nickel pack's worth.
---Brian Powell