There is a small overarching plot/idea, but since it is so vague writers are free to implement their own ideas, as well as flesh out personalities for characters.
The original art was also not really drawn that well, which also lets artists have their own take and put their own details onto the design.
The music, which if I'm not mistaken is what ZUN wanted to promote originally, was also somehow really popular for fans to make remix versions of.
Combine all that with cute girls
pokefannafekop said:
for every trope, archetype, species, height and cliche known to man.
and you get a surge in popularity.
It's somewhat like kantai collection/love-life/school idol shows, where you just make a bunch of characters and at least some will appeal to someone, but since they're all part of the show it allows many different people to get into it.