Except for Ryan Murphy, of course.

It only loosely has anything in common with Lovecraft in that there were very old religions that had little in common with what people would call "religious"(in most cultures) today.
It would been perfectly normal at one time to make any sacrifice thought necessary to keep the gods in charge of fertility, the weather or the sun appeased.
But no, there haven't been any truly cosmic entities with motives that are difficult to understand on AHS so far.

Who says that's not the case? A lot of good arguments could be made that we are indeed living in a hell dimension already, in real life. Just follow the weather reports, the clown sightings, and the American political process. XD

if evil events cause all this, than the whole world should be haunted and trapping us.

Sadly, no evidence of Lovecraftian entities yet. Not even Yog-Sothoth, although 1) there aren't a lot of ghosts in Lovecraft (closer to none), and 2) Shub-Niggurath was the Dark Goat of the Woods, not the Dark Pig, so we're not likely to see her vast and shambling awesomeness.
If any of the hillbillies get nekkid and we spy tentacles, though, we'll know they're related to the Whateleys, and all bets are off.

The reason why people get trapped is because of an evil and catastrophic event. In Murder House, it was the birth of the Infantata. In Coven, it was the presence of witches, related to Satanic activity. In Hotel, it was March's murders. In Roanoke, it was the Butcher's sacrifice.