Err... I don't know where you got that impression, but it is hardly accurate. Fantasy traditionally has had that as one small branch, but it certainly hasn't been true of the whole, or even the majority, even with "epic" fantasy fiction.
Again, I suppose this depends on what you mean by "overly violent" -- I can think of quite a few heroes of fantasy (classic and otherwise) who were quite violent, often maliciously so; and the vast majority had a fairly strong libido, going back at least as far as Howard's Conan. (True, there were no graphic descriptions of sex, but that is true of most literature until well after the Modernist revolution, and sexuality was a very strong component of those stories, and certainly of the Cimmerian's character; as opposed to, say, Kull.)
And on the subject of violence -- Elric was not only violent at times, but perverse, malicious, and cruel; outright vicious on occasion. Erekosë destroys the human race. Jerry Cornelius is both strongly sexual and perversely (and arbitrarily) violent on occasion. Airar Alvarson (Pratt's The Well of the Unicorn) casts a spell on someone he is enamored of and basically rapes her by such means. And so on....
All of this predates Martin & Co. by some years (or decades)....