BaDIK isn't just popular, it's also in a league of its own in terms of polish and it has a massive advantage to happen at a time when its more or less the only one. Roughly around the time of its release we had stuff like milfy city, summertime saga was at its peak, DMD, we were just coming off the golden age of big brother and dreams of desire etc., right now - it's just this game. Oh sure, there's amazing stuff around right now, no doubt about it, but there's no game that seriously stands above all the rest as much as this does.
Plus you really can't fault the consistency - even with updates that feel like they're milking it and aren't that great, you'll still rarely feel, you know, cheated. Some updates bored me, but I don't think i've ever been straight up disappointed at the game. That really helps retain the audience, since I can guess most of us here play like actual hundreds of games, we'll go through this one at least once - and if it doesn't LOSE any of us, it's obvious it'll have literally the entire site as its audience.
And finally, BADIK still is one of the only games currently going on that gives off a lighthearted vibe. Most devs still haven't figured out the dark, fetish-y, incest-y stuff is nice and all, but people like comedies, coming of age things, just lighter things. It can't all be corruption, almost-rape and drama. I struggle to name any games except this one that hit that sweet spot properly - I guess maybe except a man for all.