I haven't read Twilight, but I've read a few beloved and popular books that are atrociously written from a literary standpoint. That does not mean they are not popular for a reason.
One I did read, out of morbid curiosity, is 50 Shades. It's utter dreck in terms of writing quality. It's trite, it's full of clichees, and formulaic to the extreme (and incidentally a repurposed Twilight fanfic; if you wonder about the weird references to hunger, there's the reason), but if you look at why it became popular, you might notice that it is extremely well crafted for its niche.
If you don't want a "billionaire romance" (yes, this is a well defined niche; there's a reason Grey is described as one) melded with the "danger" of vampire-transformed-into-traumatised-man-with-a-dark-side, it's easy to tear it apart (I couldn't get all the way through it - it was awful along the axes I care about), but as a study in flawlessly merging two niches popular with one of the biggest book-buying demographics that have extremely predictable and rigid expectations, it's really well executed.
I'd struggle to accept it as art, but as a particular kind of craft, it is a masterpiece even if I dislike the craft in question.
You will undoubtedly find poorly executed dreck that is popular just because it happened to strike a chord out of sheer luck as well, but a lot of the time I tend to realise that if I look at something I dislike and ask what made it resonate with its audience, it turns out that a lot of it resonated with its audience because it was crafted to hit all the notes that specific audience likes.
At the same time, it's never been the case that great pieces of literature was assured doing well on release. Moby Dick, for example, only sold 3,000 copies during Melville's lifetime (makes me feel a lot better about the sales of my own novels, though I don't hold out any hope of posthumous popularity) and was one of his least successful novels when it was first published. A lot of the most popular media of the time is long since forgotten for good reason. And so we end up with a survivorship bias towards the past, where we see centuries of great classics that have stood the test of time and none of the dreck, and measure them up against dreck and art alike of contemporary media.