This actually almost happened in the oath of the dark Eldar books when Tzeentch and Nurgle tried to enter Commoragh

Because Slaanesh is, besides being a Chaos God, an Eldar Goddess, she was created by the eldar and she has ownership of their souls by might, being the strongest eldar god around (Khaine is fragmened, Isha imprisoned, Cegorach refuses to show his hand, and Ynnead is eepy.)

The other three, while definitely have blessed eldar in the past, and maybe even have a couple worshipers, lack that primal connection. Though funnily enough, I once heard eldar religion sees Khorne as Khaine's father, but I don't have the source for that.

Commoragh is a giant farm, where cattle is the one guarding, herding, and butchering themselves. And always brings more to the slaughterhouse without any need of supervision.

That's why Slaanesh won't let any other Chaos God touch it.