Well, as far as "remaking" things go (as in "rebooting" or "re-imagining") I'd say to some extent that is the whole reason to so something again. Why cast Gary Oldman as Dracula if all he's going to do is do an imitation of Bela Lugosi? The first film of Murder on the Orient Express is very good, but the second went with a bunch of changes that frankly made for a better, more compelling film. Ditto the series Battlestar Galactica. I suppose the idea is to make something more accessible, to hopefully do it better, pursue a different take on things, etc. One example I use is how the movie starring Humphrey Bogart called The Maltese Falcon was the third film of that tale (the first starred Bette Davis--no, not as Sam Spade).
As for What makes Dark Shadows Dark Shadows? And excellent, even intriguing question!
On one hand, we have the basic elements. The Collins family. Supernatural goings on amid family drama on the estate. Past secrets coming back to haunt the present, one way or another. Every clan has some skeletons in their closet, but the Collins seemed to have a whole army of the things! The characters we know--Barnabas, Roger, Liz, Carolyn, etc. Storylines we recognize--the reluctant vampire, for example.
But I would go a step further. Dark Shadows struck a chord in me particularly because it touched on that sensibility which in the 1960s was called "gothic" as in the novels of Victoria Holt and company. It echoes back to works like Jane Eyre and Carmilla and Turn of the Screw as well as The Moonstone and (to use a modern example) Fingersmith. Collinwood is like a mansion one might visit in a dream--a comfortable but isolated labyrinth full of secrets--a place both familiar and alien in some way.
Almost everyone seems normal and often in some sense nice enough. But the brother and sister who head the family each believe themselves to be murderers. One has a son seething with resentment, not least because no one believes him about the weird goings-on in his home. Another has a lonely teenage girl with a masochistic streak. The governess doesn't know who she is, quite literally. The local doctor has an agenda very different from the welfare of her patients. The charming cousin is a predator, albeit a reluctant one. The local artist is an alcoholic and a perjurer, his daughter a brainwashed rape victim, as is her boyfriend. In other words, not only does the house and grounds contain secrets, so do the characters. Every. Single. One.
But there's more to it than that.
Apart from the props, the familiar characters, the trope of all those secrets and people trying to keep/discover them, there's also a flavor to Dark Shadows, one somewhat Victorian and yet American, one that tastes of Autumn and Winter rather than Spring or Summer, something rather Yankee and intense--with metaphors and archetypes we all recognize. The matriarch. The dillitente. The rebellious teenager. The byronic hero. The woman scorned...
