Let me come at this from the perspective of a long-standing Ranger fan (50+ years). First, I absolutely, positively want the Isles to survive and thrive in the New York area. There is no better rivalry in all of sports than the Rangers and the Isles. What sets the rivalry apart is, not just the close proximity of the teams, but the presence of opposition fans in the other team's building. Losing the Isles to Quebec or elsewhere would be a terrible thing for NY hockey fans no matter what their allegiance.
Second, there is no doubt that hockey is the #4 sport in the NY metropolitan area: just listen to sports radio for a day and you will understand that. But that doesn't mean that there isn't a large population of passionate, dedicated hockey fans. In my long devotion to the sport, I have seen the phenomenal growth of hockey on the youth level, with many high schools (at least in the northern suburbs where I live) icing teams whereas 20+ years ago, just the thought of organized hockey, was an afterthought and scoffed at. So is NY a hockey town? In its own way, absolutely.
Next, the Islanders have always been fascinating to me in a larger-than-on-the-ice way. My internal question has always been: can a suburban team, not an urban team playing in a suburban arena but a truly suburban team, survive supported by a suburban population, suburban business, suburban media, etc.? In my mind, the jury, even after all these years, is still out. Yes, LI has a large, passionate hockey base. To say that LI is not hockey country is just absurd. There is a long tradition of hockey on the Island going back at least to the old LI Ducks of the EHL (Buzzy Deschamps, anyone?). One of the reasons the NHL expanded to LI (aside from the threat of a team in the WHA) was that hockey was established on the Island: the Rangers practiced there and most players lived there. But the question has always been, could a team grow there supported by "casual fans" in non-winning years? I don't know. The situation was not helped by, as the years went by, by an old arena, the lack of public transportation, the loss of manufacturing jobs (Grumman, for example), ownership problems,etc. I still don't know. As an adjunct to that is the question whether a truly suburban franchise be attractive to free-agents or a team's own pending free agents. The Islanders, unfortunately, have often seemed as a hockey backwater to me (but not as bad as the Devils), that was only attractive to players who could not get deals elsewhere. This was what was fascinating to me about the move to Brooklyn: they would now be an "urban" team is a part of NYC that is booming. Unfortunately, the situation at Barclays, has become untenable. So the jury is still out for me about the long term viability of the franchise in a suburban situation. I want to see it do well there (hey, I live in a suburb myself), I think it can, if all the parameters of success are met (including having a team that is consistently good and makes the playoffs yearly), but I still entertain doubts. I do know that losing the team would be a horrible thing for all NY sports fan.
Last: the possibility of an arena in Belmont. It is easy to be optimistic about the possibility except for the reality of NY politics. Nothing gets done without politics in NY, on the local and state level. There are multiple issues, aside from on-ice issues, that could derail this arena: so many power-players with agendas, so many power brokers, etc. I am minimally familiar with the area: generally I am only there once a year (there are some large cemeteries nearby in Elmont, not Belmont, where I have grandparent buried). So, once a year, I pass by Belmont Racetrack. It just seems an out-of-the-way area. I know the LIRR has a stop: but isn't it a spur from a main line? (I don't know, just asking). Would the LIRR run trains on game nights to the station? Would it be easy to get to from other places on the Island using the LIRR? I know most people would drive: but Belmont is right on the NYC/LI border. With the usual problems of traffic congestion on the Island's highways, what would it be like driving there on game nights? The Coliseum seemed more centrally located for Islander fans (an advantage), Barclay's has mass-transit and an urban setting (a perceived advantage): Belmont just seems so out-of-the-way and, even in the context of the urban/suburban sprawl of Queens/Brooklyn/Long Island/the Metropolitan area where nothing is really out-of-the-way.
Anyway: just some random thoughts of a long-time Ranger and hockey fan who livex in the northern suburbs, but wants the Islanders to find some solution that would allow them to survive and thrive.