This is a question that was raised in a series of email dialogues with a few friends. One in particular is concerned about the role of Asian philosophy in the American philosophical market (a concern I share as well), and about his ability to get a job as philosopher of Japanese aesthetics and religion. He's actually studying the influence of Non-Japanese religious and philosophical concepts on the Japanese idea of mono-no-aware, an idea that is interesting, controversial, and that should provide plenty of scholarly depth and research.
The problem, however, is that in terms of marketability, he would probably be better suited in an East Asian Languages and Culture program. I've encouraged him to apply, and I hope something works out for him. Given that things might not, this naturally raised questions and concerns about the nature of the American academic market, whether contemporary American philosophy has any use or interest for Asian philosophy in general, and (for me, at least), the degree to which the two can engage in functionally productive conversations on shared topics of interest.
First of all, one of the immediate problems in studying Asian philosophy is that the American academic market isn't even convinced that Chinese and Japanese traditions produce something called "philosophy." The evidence here isn't simply anecdotal: there's no standard understanding of how eastern traditions fit into the administrative structures higher education. The number of programs that actually allow for the study of east Asian philosophy qua philosophy is relatively small.
Both East Asian and South Asian philosophy have traditionally found their homes in religious studies programs, departments of religion, or departments of east asian religions and language. These latter are in all honesty probably provide the strongest opportunities for studying eastern thought, as it requires understanding different modes of discourse, different cosmologies, and usually at least two other languages (Chinese and Japanese for East Asian, and German and Sanskrit for South Asian).
However, this also seems to have the effect of keeping contemporary American philosophy removed from the concerns of eastern thought. Religious beliefs about ancient cosmologies, after all, are not really the concern of contemporary philosophy. As such, contemporary American philosophy (philosophy of mind, philosophy of science, philosophy of language, etc) can thus safely disregard the ideas and beliefs of eastern traditions.
On a more practical level, attempting to move beyond simple comparative philosophy is actually an extremely difficult task. Introducing an entirely new vocabulary to a conversation already in progress is not only disorienting to the original members of the conversation, but is often viewed as anti-productive and self-serving. The other problem is that the concepts in many eastern traditions are based on views of personhood and language that are so fundamentally different from the models already in use in many western debates that attempting to use eastern terms often results in being bogged down in lengthy discussions about cosmology, moral relativism, and incommensurability.
This wouldn't be such a frustrating issue to me if I didn't feel like Asian traditions actually have a great deal to say to western traditions. The recent development of moral psychology could benefit immensely from dialogues with Hinduism, Buddhism, Daoism, and Confucianism. Political and social philosophy is another area of immense importance, as eastern traditions don't just grapple with problems of intersubjectivity, but are all predicated on assumptions of intersubjectivity. The resultant models of personhood found in asian traditions of thought are simultaneously nuanced and complex, and further study by western traditions in general would reveal many insights and resolve many issues still under struggle. Models of aesthetics as well would benefit, as Eastern thought in particular eschews subject/object relations in art and instead focuses on the dynamics of aesthetic experience and the transformative power of gesture or word.
This is just a small list of the possible benefits, and I think it's worth stopping here for the moment. One direct for further conversation would be to discuss these particular areas in more detail, and provide more specific examples. Another direction for further discussion would be to discuss more complicated areas, such as philosophy of science and technology. And finally, I still want to eventually address my ultimate concern, which is the nature of incommensurability and the challenges of actually engaging in cross-cultural philosophical dialogue.
Here's a spoiler: the biggest problem is often identifying a shared problem, and convincing all the interlocutors involved that the problem is common across different traditions.