You can say "they are the doctors" -- but yeah it's a slightly different meaning.

BTW in German, it's a fun distinction. The old "ich bin (ein) Berliner". (or hamburger or frankfurter...)

Works in English too:

* I am Danish.

* I am a Danish.

Or

* I am dancer.

* I am a dancer.

“I am dancer” is acceptable if you’re a five year old. However “I’m Danish” is correct English