Given that in international law it exists between courts of different jurisdiction while in arbitration the public policy comes in especially with the issue of immorality.
trade agreements are only enforceable if both parties are subject to the same treatment in arbitration. Most trade treaties involve a third party in order to settle disputes. Comity become problematic when the foreign policy conflicts with domestic policy. For example, for the TPP, there is a section on investment protection that allows investors to sue states if they enact laws that would hurt their investment and therefore affect the creation of laws. Of course the United States would be obligated to allow this to occur but the country is also obligated to protect its citizens from from "things" that affect the well-being of its citizens. Then there is the mentality of "you scratch my back, I scratch yours". This would involve the national government to be involved in the decision making powers of the judicial system of their respective country. Now I do not have to tell you how unconstituional that would be in the United States but you get the idea of how problematic comity could be