I have never been quite clear about what "studying" littacher means. (I do know the difference between aggressive reading and passive diversionary reading.) However, there are a few "critics" - I think of them as "illuminators", who are wonderful to read on the topics of books and authors. Books about books, which are literary works in themselves. Harold Bloom is one, another is John Updike, and I can list a few more who I enjoy like Edmund Wilson, Lionel Trilling, Walter Benjamin.
I also enjoy learning from experts about how stories (or songs or pictures or poems) are structured, the hidden architecture.
In the end, people do love well-told stories and well-depicted ideas and things, regardless of the medium. When stories, for example, are very well-written and constructed, the delight in the words adds a lot to the tale (eg rosy-fingered dawn). Craft, talent, inspiration, penetrating intelligence, wide knowledge, insight into human nature, magic - the things most of us lack but admire and even envy.
I would take a class with Bloom, but what about "studying littacher" in an ordinary high school or college? This via Schneiderman's Are Literature Departments Doomed? (but not his view):
Literary texts, like other artworks, are neither more nor less important than any other cultural artifact or practice. Keeping the emphasis on how cultural meanings are produced, circulated, and consumed, the investigator will focus on art or literature insofar as such works connect with broader social factors, not because they possess some intrinsic interest or special aesthetic values.
Bullshit.