The same statement can be applied to the 2000s Rangers, who were mired in mediocrity for well over a decade, and are owned by one of the worst owners in all sports, James Dolan.
Somehow, a team owned by a worse version of Pegula managed to turn it around, so there must be hope for a Sabres team that has historically been competitive enough to compete in the playoffs, and still has one of the highest regular-season winning percentages in the league even after the tank years.
The answer to your question of why losing Eichel would be fundamentally unacceptable to Sabres fans, and most importantly, season ticket holders, is because this would be a worse offense to Sabres fans than trading ROR, and even worse than the Sabres not signing Chris Drury and Daniel Briere after the 2006-2007 President's trophy season. The Sabres finally have a true franchise center that they haven't had since Gilbert Perrault when the team was first formed, trading Eichel in his prime for scraps on the heels of trading a Conn Smythe and Selke trophy-winning ROR would be a death knell for a small-market team. Fans would lose interest at a rate a small-market team like Buffalo would struggle to compensate for, especially after season ticket renewal rates have finally started declining after holding steady at 98%+ year-after-year all through the tank years--the reason for that is because of Eichel, without him, renewal rates will nosedive.