We credit Shakespeare more as being a great play author, rather than a poet. Why do you think so many critics neglect his sonnets when studying his work?

A very interesting question. Possibly, we can credit this bias on the part of critics to the fact that Shakespeare himself seems to have identified himself more as a dramatist than as a poet. While his plays certainly are known now for their revolutionary use of language and express his poetic qualities, they are seen as championing his skills as a playwright, rather than as a poet. Meanwhile, various poems from Shakespeare's sonnet cycle live on as great and famous love poems, but it remains the case that Shakespeare wrote only one set of sonnets—all connected to each other, and written over the same period of time—whereas he wrote 37 plays over the course of his entire career.
Furthermore, while there are points of uniqueness about Shakespeare's sonnets—his poems to the Dark Lady critique the typical presentation of a loved one in romantic poetry, for example; while his love poems to the Fair Youth are a unique representation of homosexual desire from this period—they do conform, very often, to accepted structures from the Elizabethan age. Shakespeare's plays, by comparison, stand alone. In his plays, as in none other from that era, we see people from all ranks of society represented as equally human. We can assume that this is, in large part, due to Shakespeare's own background: as a man without a university education, he was unusual among writers of his day, and through him we see a representation of society that was not present in other drama of the period—or for much of the time that followed.