"I'm a doughnut?"
Wot?
“Ich bin ein Berliner” is, at worst, ambiguous and somewhat awkward. It's hard to think the listener would have construed the noun “Berliner” to mean a pastry in context. I remember seeing the speech on TV news at the time and the crowd went wild.
By the way, JFK didn't say he was a Berliner, he said that the proudest words a person could say were once “Sum cives Romanus.” but today they were “Ich bin ein Berliner.” He was praising Berlin for being in the forefront of the struggle for freedom.