Students can write to explain professional concepts, positions, or policies in letters of application or letters to politicians.
Students can also write business letters of introduction and research gathering, introducing their projects and plans for approval. Another version of an introductory letter could have students try to persuade an interested party (e.g. a foundation, the NSA, etc.) to provide funding or approval for their research. Or have them write a letter after completing a project which tries to persuade someone interested in the project to accept their recommendations.