The reason that a student should study Romantic poetry is probably similar to why a student should study Victorian poetry or Modernist poetry. Romantic poetry represents a different caliber of writing. A student should study Romantic poetry because, as a movement, Romantic poetry was a "game changer." Romantic poets redefined the contours of what poetry could be. The Romantic poets transformed how individuals viewed poetry, and art, in general. Students should study this in order to see how poetry was transformed and its effect today.
Outside of this, I think that Romantic poetry offers some unique insights toward which students can gravitate. The Romantic poets' stress on subjectivity and freedom was essential to Romantic poetry. Students who are seeking to enhance their own subjectivity and freedom can find much in Romantic poetry. In this regard, Romanticism can have much in way of meaning to students. Another reason was the varied nature of the movement. For example, in the British Romantic tradition, the works of Coleridge and Wordsworth differ in scope from the works of Byron and Shelley. The works of Keats are different from all others. Students can gain much in way of insight and thought when they are exposed to this divergence of poetic expression. Students can also understand that any movement can have different aspects to it. In this appreciation, students' insight and analytic skills increase. These would be fundamental reasons why students should study Romantic poetry.
We should read Romantic poets for the reason we should read any literature, we learn more about ourselves through it.
Romantic poets are fascinated with the sublime ("inspiring awe"), which is what makes them so interesting and worth reading. While Wordsworth, Coleridge, Shelley, and Keats (especially Keats) are all quite different than one another, they all concentrate on observing the outside world to then look in on themselves.