Oh, I'll fully admit that EH has flaws. I find it too random, for one. But then, I come from strategy and roleplaying games, where we usually try to eliminate that.
As for repetitiveness of the mysteries... I'd say there's more than three types. Let's try to classify them...
*Go to place, do special encounter set
*Do research, gather clues. Subsets: go to location, then spend clues.
*Close gates, and variants
*Kill monsters. Subset: kill epic monster, kill number of monsters
*Find specific artefact, often in combination with special encounter, kill monster or spend clues.
That's five types. Not great, I'll admit. Still... I'm not sure how one would improve this. I mean, look at Arkham. THere's one and just one win condition, close gates. I still prefer having several.