In my country, government applications are required to be interoperable, use open APIs and work with open formats (XML, PDF, etc.). There should be no problem there. I've already used some FOSS applications to interact with government services.

Banks are required to interoperate using open API in the EU. EU managed to cripple this requirement, by not requiring open api access to regular customers, but only to accredited organizations. There's more work to be done on this front.