In Daniel D'Addario's un-called for hit piece, he refers to Lady Sybil's death as her punishment for having married below her station. He also claims that the show seems determined to prop up Lord Grantham as a wise patriarch. He is, of course, wrong on both counts.
Lady Sybil dies because Lord Grantham, who is always portrayed as a rather foolish old man, unable to cope with the changing modern world, refuses to listen to the simple country doctor who has treated Sybil since infancy. Instead, he sides with the more prestigious Sir Philip, who turns out to be tragically wrong. Lord Grantham, wedded to the old class system, insists that the doctor from the upper caste, the man with the title, must be right, even when Cora recognizes how wrong he is, and begs Lord Grantham to listen to Doctor Clarkson.
So Lady Sybil dies, not as punishment for her betrayal of the class system, but because of Lord Grantham's fealty to it. Clinging to the class system cost Lord Grantham his daughter, not exactly a ringing endorsement of the class system.