Could the US passport indicate any nationality other than USA?

No, the nationality field on a United States passport can only be "UNITED STATES OF AMERICA." This is because a passport is an official document issued by a country to its citizens, and it is used to verify their identity and citizenship when traveling internationally.

The purpose of the nationality field on a passport is to indicate the issuing country of the passport. In the case of a United States passport, the nationality field indicates that the passport is issued by the United States government to a citizen of the United States.

Sources:

U.S. Department of State, "What is a Passport?" https://travel.state.gov/content/travel/en/passports/what-is-a-passport.html
U.S. Department of State, "U.S. Passport Card FAQs" https://travel.state.gov/content/travel/en/passports/how-apply/cards.html#1
I hope this helps answer your question!

There are travel documents resembling passports for people who do not have a nationality, or are "stateless".

An example from Germany can be found here.

The document format and page layout resemble a passport. The cover page contains the logo "BUNDESREPUBLIK DEUTSCHLAND" with the Eagle icon. This could potentially be taken for a passport, so that an explicit nationality field (which in this case reads "STAATENLOS GEMÄSS KONVENTION 1954") is helpful to avoid erroneous readings, as Kate mentioned.

On a side note, if it’s always the same, why is it mentioned?

Some countries have different classes of citizenship, largely due to their colonial history. For example, a British citizen would hold a British passport (code GBR) with nationality as "BRITISH CITIZEN".

A citizen of Bermuda, for example, would hold a British Passport, that has the same cover with the words "Government of Bermuda" on the front. Inside, it would have code GBR but nationality as "BRITISH OVERSEAS TERRITORIES".

As a British Overseas Territories citizen, they would be entitled British consular assistance, but would not have permission to reside or work in the UK. That person would also hold Bermudan residency status, to enable them to live and work in Bermuda. If they wanted to move to the British Virgin Islands, they would have to acquire BVI status.

There are other situations like British National (Overseas) status, for those who wanted to retain British status after the handover of Hong Kong to China in 1997. The BN(O) passport has the same cover as the British passport, but again, the "BRITISH NATIONAL (OVERSEAS)" nationality indicates limited rights to reside in the UK.

My main question is, can Nationality on a US passport state anything other than "UNITED STATES OF AMERICA"

No, since even before the 1856 enacted passport statute, passports issued by the Secretary of State for travel outside the United States, generaly contained the text that the person is a "Citizen of the United States".

The United States Passport: Past, Present, Future – United States. Passport Office (1976) – Google Books

• PDF page 50:

In 1856 Congress enacted what remains today as the basic passport statute.

This law provided that the Secretary of State be authorized to grant and issue passports, and cause them to be granted and verified in foreign countries by diplomatic and consular officers of the United States under such rules as the President might prescibe. No one else was to issue passports, and they must be issued to none but citizens of the United States.

The Act of 1856 also made it a penal offense for a consular officer to issue a passport to anyone who was not a U.S. citizen.

1824	1923

On a side note, if it’s always the same, why is it mentioned?
I would appreciate any sources.

This is due to the norm set out in the 1920 League of Nations Passport Conference ¹, where it contains the wording:

in the event of a passport being issued by a Government to persons other than its nationals.

Until 1914 passports could be issued to non-nationals and sometimes done for residents.

During the 1920’s, this praxis was replaced with the general rule that passports should only be issued to nationals (introduction of the ‘foreigners passport’ in 1922).

Some countries still have different grades of citizenship.

A UK passport can contain British citizen or subject, with the holder being treated differently based on that entry.

¹ the present day ICAO recommendations are based on these norms developed during the 1920’s

Passports all have that field. It enables officers to flip to the picture page and get every piece of information they want in a consistent format. (Plus the various machines that scan passports at checkin and the thing they slide your passport through that reads the characters at the bottom of the page.) All the Canadian passports say CANADIAN in them (plus CANADIENNE). (To see an example, expand the Canadian Passport section of this government page about ID.) If it wasn’t there, because it’s obviously whoever issued the passport, then the officer would have to look elsewhere (eg the front cover) to see who issued the passport, and machine-scanning would be harder too.

Bottom line: while it’s the same for all US passports, it’s not the same for all passports the people who look at passports see every day.