In general, one could say that there is and there isn't much collaboration in American poetry today. As I've defined collaborative poetry, there isn't too much of such work going on, especially on the level of book publishing, which makes Reb Livingston and Ravi Shankar's Wanton Textiles, as well as the postcard poems of Tim Yu and Cassie Lewis, relatively unique works of art. But I would say that there is a lot of collaboration among poets in other forms -- for example, writing workshops and conferences, feedback from poetry editors, suggestions and critiques from other poets and friends. You could even expand this list and point out that poets live in societies and are greatly influenced by the time and place in which they live. I would thus assert that the notion that poems typically exist in some kind of "pure" form, uninfluenced by the opinions of other individuals, is somewhat overly romanticized and outdated. In this sense, I think that most poems are the products of a certain degree of collaboration among poets.
But in the less abstract sense of "collaborative poetry," I find it interesting that there is almost none of that happening in Asian-American poetry today. I think that it points to the importance of the individual in the generating of poetry, especially poems that are more personal in nature. But I also wonder whether such a lack of collaboration is essentially a byproduct itself of a particular tradition in contemporary American poetry that presumes a poem to have only one author and thus approaches collaborative poems with some measure of bewilderment. In other words, if you read enough poems in literary magazines that have only one author, pretty soon you presume that is the way that poetry works.
From both history and modernity, however, we know that there are different ways in which the art of poetry could and does work. In some Asian cultures, oral history is the primary means through which poetry is generated, shared, and passed down from generation to generation. The renga is a form of collaborative poetry that originated in Japan, and poets throughout the world continue to work in the form today. Then there is the whole concept of "postcard poetry" in which, in its simplest form, poets exchange poems on postcards, which may or may not touch upon specific geographic locales depending on the poets' definition of such poetry.
While I think that most poets who engage in collaborative poetry find it amusing and a nice change of pace, I also think that such work can and should be taken more seriously as well. There are many potential upsides to collaborative poetry -- it could point to similarities and contrasts in writing styles between two poets, work as a means to highlight different perspectives on particular issues, like matters involving race or ethnicity or gender, and help poets grow as authors and thinkers by showing them a different way of approaching a topic or theme.