Proper adjective, or noun with Indefinite or zero article, when defining national identity?

Why is it mostly a preferred option to use an adjective as a subject complement when it comes round to national identity whereas "American" can be both a noun and an adjective?

I am American

Why not: "I am an American".

Even more complicated is with a pattern like:

I'm Southern UK

why not: "I'm a Southern UK"?, "Southern" is an adjective and UK seems a noun but only at first glance.

It all gets clear when there are only adjectives for naming the aforesaid:

I'm French (Belgian).

And as for the Poles there are different parts of speech that can be used:

1. I am a Pole (and it can't be changed to "I'm Pole)

and

2. I am Polish (and it can't be changed to "I'm a Polish).

Actually a US citizen can say "I'm an American". In fact there is a George Gershwin composition, a song and a 1951 film all called "An American in Paris" but 'American' used as a noun in this way is actually a shortened form of "American person" or "American citizen" (and 'American citizen' is, strictly, a synonym for "citizen of the United States of America" since Canadians, Mexicans, Brazilians, Agentinians and inhabitants of all the other countries in both American continents are Americans in one sense).

If we say "I'm an X" referring to our nationality then X has either to be a noun or an adjective accepted as a noun (as American is). Only certain adjectives have acquired this status and 'British', 'Polish' and 'French' are not among them.

It is actually arbitrary whether an adjective has this status, most of the ones that end in 'an' (Jamaican, German, Russian, Australian for example) and 'i' (Israeli, Saudi, Pakistani and so on) are acceptable but those ending in 'ish' are not. I have no explanation for this, it's just the way the language has developed.

You will find, though, that nationalities whose adjectives are not acceptable as nouns tend to have specific nouns for their citizens, even if they are informal. Think of "I'm a Frenchman", "He's a Brit", "She's a New Zealander (or Kiwi)".

Edit After thinking about this a bit more I've realised that the convention ruling when national and ethnic adjectives are acceptable when acting as singlular nouns is probably related to whether such nouns are used as plurals in other cases. For instance we say "The British have bought a lot of properties in Spain" which means that 'British' as a noun is considered to be plural (or perhaps a mass noun) so "a British" is unacceptable. However we say "The Americans landed on the moon" using the plural form of the noun so, when we are talking about one person, we can say "The man in the Bermuda shorts is an American" because there is a singular form of the noun available.