It's really not all that surprising that the Daycare Attendant ended up being so popular, to the point that there's a whole subsection of FNAF fandom that's p much just the DCA.
For starters, there's Security Breach itself. Security Breach is a vastly different FNAF game from its predecessors. Instead of being a jumpscare-driven task management simulator, it is a free-roam exploration and puzzle game, also with jumpscares. Instead of a security guard with their butt glued to their office chair, you're playing as a kid trapped in the mall. That difference in format and story setup attracted a whole new crowd of players to FNAF.
Next is character design. Unlike the majority of animatronics in the killer robot furry franchise, the DCA is a lanky, vaguely human shaped jester with a dinnerplate head and a creepy fixed smile. That appeals to folks who might not be as much into the robot furries, but like lanky creepy jesters (I am one of those people).
Security Breach also FINALLY develops the animatronics into actual characters, rather than interchangeable jumpscares. It's not a coincidence that prior to SB, the most popular animatronic was Springtrap-- an animatronic outright possessed by the defacto main antagonist of the series. I still remember the sheer fuzzy excitement upon hearing the first teaser trailer where we found out that we would be playing as a kid and that Freddy was our friend. That's still so cool! Freddy is our friend!
But character is where the Daycare Attendant really blows everyone else out of the water.
Sun is, after Freddy and Vanessa, the NPC with the most lines of dialogue (ten). Sun and Vanessa are the only antagonists that speak directly to Gregory, rather than just having vague hunting lines. For comparison, of the Glamrocks only Roxy has a single line of interaction with another animatronic ("Get out of my room, Freddy!") and her pep talk in the mirror at the start of the game. Monty and Chica might as well be interchangeable, both only having hunting lines.
Hell, out of Moon's nineteen voice lines, eight of them are laughs, blowing away Vanny's whopping two lines in the entire game.
Sun is the only* FNAF antagonist that does not have a jumpscare sting when he grabs Gregory, and is one of the few antagonists that does not kill the player upon jumpscaring them. Sun is outright non-hostile towards Gregory, coming off as overbearing but genuinely friendly. In a FNAF game.
Kellen Goff's phenomenal voice acting further fleshes out the DCA's character, giving us solid foundations for their personalities. Sun is anxious, friendly, and bossy. Moon is a downright giggle gremlin, sadistic and playful. Both of them are childish, and the contrast between their personalities and their job as child caretakers makes them stand out even more.
It's also worth mentioning that the Daycare is one of the earliest sections of the game, easily reached within the first thirty minutes of playtime. This makes it very likely to have been seen by people who either ended up not finishing the game itself, or any let's play series they were watching. It's also one of the most complete sections of the game, with clear, easy to understand mechanics and a decent challenge, making it more enjoyable to play than some of the later puzzles.
So, yeah. Why wouldn't there be a whole subsection of fandom built around some of the most well developed and interesting characters in the entire franchise, from an installment that attracted a new crowd of people who were probably already looking for something different from the traditional FNAF experience?
*As far as I know there are no other FNAF animatronics that perform a jumpscare animation without an accompanying sound, but it's not impossible that there's someone in UCN that I've overlooked.
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