It's not worth arguing over but Elfen Lied is (in my eyes) the worst anime I've ever sat through. I've never understood people's enthusiasm toward Elfen and it's characters when everything about it is so blatantly shallow. It tries so hard to be messed up that by the halfway point they have to cut a little girl's limbs off and beat a puppy to death to attempt to get a rise out of the viewer. It barely even starts before it stops being horror and veers toward comical. It's not relatable, it's edgy for the sake of being edgy and no amount of blood pinatas or nudity can make up for such a severe lack of talent or make it stand up as a deep or mature anime alongside the likes of Evangelion or the work of Satoshi Kon (or Ghost in the Shell, I guess).
This is just how I felt about it though, I wont forcefully try to convince you that something is shallow or soulless if it meant something to you. With that list I can see you're fairly inexperienced with anime (and perhaps to serious or "deep" art in general?) so maybe you'll see why Elfen Lied fails to impress most people once you have a better reference point. In my experience Elfen is beloved exclusively by young teens who simply have nothing that's actually good to compare it to. Hence why "entry-level" gets thrown around so much an an insult, like that other guy helpfully demonstrated in this thread.
I don't want to keep bashing something you enjoy here, but try watching Neon Genesis Evangelion. A show that, imo, excels everywhere than Elfen Lied falls flat. They're prime targets for comparison (along with Mirai Nikki, which you might like as it's essentially this decade's Elfen Lied) for both being "messed up" with deep characters, but to me Eva is so far ahead of EL in every aspect. The majority of the hate for Elfen most likely just comes from people who saw Evangelion first, which came 9 years earlier and achieved so much more. I haven't read the manga and it may well be the story that the anime wanted to and should have been, but with how much I disliked the show I doubt it would change my mind.