Should we start calling countries what their people call them?

Does it still make sense to call countries by names other than what their own people call them? It would seem to make a lot of sense. Two examples that spring to mind are Deutschland and Nippon.
In this day and age, does it really make sense to continue calling countries by other names? People are rapidly becoming more international, so having different names for countries seems confusing and counter productive. I tell people I live in Nippon and they say they've never heard of it. My Deutsch friend had the same problem when he visited the United States.
What do you think?
I'm sure a bunch of readers here could do without ever hearing "Los Estados Unidos" again.
In this day and age, does it really make sense to continue calling countries by other names? People are rapidly becoming more international, so having different names for countries seems confusing and counter productive. I tell people I live in Nippon and they say they've never heard of it. My Deutsch friend had the same problem when he visited the United States.
What do you think?
I'm sure a bunch of readers here could do without ever hearing "Los Estados Unidos" again.