Sure, there are some countries around the world that have a banking element to their post office, but typically where they do that has been a part of the postal system since its inception and the banking system effectively grew up around it, so it already occupied a part of the market.
I'm not aware of any instances in a developed banking market with effectively universal access to banking and universal ownership of accounts of a post office being able to interject itself successfully in that market and do so in a sustainable manner.