Country's "Real" Name

On the subject of languages, I’ve been wondering why we do not call a country by the name that the country calls itself? For example, Japan would be “?? Nihon or Nippon”; Spain would be “EspaƱa”; and Germany would be “Deutschland”.

I think using the country’s internal name would engender a sense of community and increase cultural understanding. It could also help people to learn a new language because we would be exposed to more sounds than we are now.

The only problem I see is in countries with multiple languages (think India), there may be a number of internal names. However, if people would take the time to learn the name of your country, you may be more motivated to come up with an official name.

Good idea? Bad idea? Am I missing something?