This was the root of the overblown Kennedy gaffe where he said “ich bin ein Berliner” instead of “ich bin berliner.”

The thing is that doesn't even sound wrong and I don't think any native speaker would object to the article when used with a place of origin/belonging in a speech.

It emphasizes the statement if you ask me.

Only many years after learning of the speech I read online that it's allegedly "a gaffe".