The convoluted build configuration automation model (EnvDTE/EnvDTE80) and its diagram was already so tricky to add / delete solution configurations that it has to explode from some angle: the lack of direct (*) support to add / delete solution platforms:

PRB: Build solution platforms cannot be added / deleted from a Visual Studio add-in
http://www.mztools.com/articles/2013/MZ2013009.aspx

(*) There is a kind of workaround creating project platforms propagated as new solution platforms (via EnvDTE.ConfigurationManager.AddPlatform(newName, existingName, true) that I will explore in a new post / article.