I was born and raised in Hamilton. Unfortunately I'm more on the younger side in terms of age so I can't be 100% accurate about things that happened before the 2012-13 lockout, since I got into hockey by the time the NHL started the season.
In my opinion, hockey in Hamilton is what football is in Toronto. The Argos are largely ignored by the city, but they do have a small, yet passionate die-hard fan base. However, they are ignored because the general sports fans in Toronto typically see the CFL as "beneath" them and would rather see the NFL come to Toronto, and then they would really support their football team.
I think this is the same with Hamilton. Both iterations of the Bulldogs did have hardcore fans, but not a whole lot. They never had an average attendance per season climb to 6k, and they were playing in an arena with seats of 17k.
I'm making assumptions here so be skeptical. I think what happened is after Balsillie got told to piss off by the NHL for the last time, most of the hockey fans here became jaded and just gave up on the NHL. You have to remember that he spent about 4 or 5 years trying to buy an NHL team and move them here, and even before that Ron Joyce put in a bid for a Hamilton expansion team in the early 90's but he didn't have enough money to pull through. Hockey fans in this city were being told by potential owners for about 15 years that they were going to have an NHL team, only for it to never happen. I think people here just had enough and decided to move on.
That's not to say that all hockey fans have truly given up, but for most of those who are still hockey fans, I do believe that they are in the "NHL or bust" camp. I would also imagine that those who were holding out for the NHL fifteen years ago are also in the "NHL or bust" camp even if they don't care about hockey anymore. Again like Toronto and football, the bulk of hockey fans here are not willing to support any non-NHL team that makes their way over, and this is particularly amplified since they were genuinely close to landing NHL teams a few times before it ultimately never happened.
This is also why I think the OHL Bulldogs were eventually going to leave one way or another. They never had good consistent fan support. The most they ever averaged in a season was 4,251, and it's likely that their average attendance per season numbers are skewed because of school day games. Their playoff attendance wasn't great even in the championship years, and it was only until the final round that the arena started to really get full. The unfortunate part is that the Bulldogs were well-promoted in the city (or at least I think they were), but the bulk of hockey fans didn't care. They tried a "Hamilton Is Hockey" marketing tactic and it didn't stick. Adrian Tracy (local hero as a defensive end for the Ticats) showed up to at least a few playoff games in 2018, though the fans in attendance weren't too interested. The Ticats themselves tried to hype up the Bulldogs, and again it didn't stick. People just didn't care.
I'm curious as to what would've happened if Andlauer was able to get his 5k seat arena which would've been on the Mountain. The bulk of people live in Downtown, but they probably would've been able to draw from places like Brantford and such. Downtown Hamilton isn't exactly the nicest place around and I'm sure that's a sentiment echoed by traveling OHL fans. Maybe they would've been better off, or perhaps it would be a waste and there still wouldn't be any consistent fan support. I don't know for sure.
One last thing. When the Heritage Classic came by here, I swear there was absolutely no promotion about it in the city whatsoever. If you were in the city and you didn't know beforehand that the Heritage Classic was happening, the most that would happen is it would get mentioned to you in passing by somebody. 26k people showed up to the game, sure, but how many of those do you think were already living in Hamilton, compared to the travelling fans from Toronto and Buffalo? I'd honestly presume not too much. 12k people showed up to the OHL Outdoor Classic the day after, and like usual, the Bulldogs lost that kind of fan support after the game. The only time they saw a crowd like that for a game again was for Game 7 of the OHL finals, when I believe it was 11k people that showed up.
Anyway I apologize for going on and on and writing a whole lot. I just wanted to explain as a resident of the city what I believe is the general consensus among hockey fans here. My message isn't to explain why or why not Hamilton should have an NHL team like the bulk of hockey fans here think, it's simply to explain how I think they feel. My feelings are irrelevant in this matter. This also isn't an answer as to why OVG is willing to put an AHL team here when past hockey endeavors haven't typically had long-term success (save for the Bulldogs). Regardless, I hope this helped and I'm happy to be corrected by anyone who lives in or around the city with opposite experiences and feelings.
TL;DR:
@stealth1 is likely right in that the majority of hockey fans in Hamilton will not support any level of hockey that is not the NHL;
@WeaponOfChoice conveyed that accurately.