Actually, it was only two generations that have come and gone. XY(gen 6) and SunMoon(gen 7).
I'd like it if all those fans would stop and remember that this is just a video game that a big corporation is wanting to sell them.
Animal Crossing, while it started out as series that got a game every three years or so, quickly stagnated with City Folk and Nintendo realized this. New Leaf tried something new with the formula, but it took time to rethink the gameplay and freshen it up. It worked wonders for them, so future releases are definitely spaced farther and farther apart now because they know they can't just pull a Game Freak and release a new game with minimal updates. We'll be looking at another good 6 to 7 years before the next game as well.
Premature reactions and declarations are highly immature, and threatening to riot? Seriously? I'm thinking the fanbase is either very young or most had started with New Leaf and thus have no idea how game development works. Things take time.
And to boot, Nintendo didn't actually announce THE Animal Crossing game in September, but the fact they - A - game in the series was in development.
For comparisons sake, we know a big new mainline Zelda is in development, they have told us as much. They didn't make a spectacle about it like they did with Animal Crossing though.