The requirement to have radio licenses originates from the International Telecommunication Union (ITU), an international organization responsible to manage the allocation of radio frequencies. They are also responsible to regulate the use of transmitting equipment with a view to ensure they operate within acceptable tolerances.
ICAO Convention Article 29 details the documents that each nation is supposed to require for all aircraft. The ICAO Standard specifically states a radio station license and operator’s permit are required if the aircraft is equipped with radios. Although ICAO rules are not the law of the land, the nations that are signatories to the Convention agree to either follow the ICAO rules or let ICAO know that they have a “difference” with the ICAO recommendations. The United States (U.S.) is a signatory.
In the U.S., the Federal Communications Commission (FCC) sets the rules. They do not require U.S. registered aircraft flying in U.S. airspace to have a radio station license; however, they do require U.S. registered aircraft that are flying outside of U.S. airspace to have a radio station license.
Here is what the FCC regulation says:
Title 47: Telecommunication, PART 87—AVIATION SERVICES, Subpart B—Applications and Licenses
§ 87.18 Station license required.
(a) Except as noted in paragraph (b) of this section, stations in the aviation service must be licensed by the FCC either individually or by fleet.
(b) An aircraft station is licensed by rule and does not need an individual license issued by the FCC if the aircraft station is not required by statute, treaty, or agreement to which the United States is signatory to carry a radio, and the aircraft station does not make international flights or communications. Even though an individual license is not required, an aircraft station licensed by rule must be operated in accordance with all applicable operating requirements, procedures, and technical specifications found in this part.
U.S. Customs has been given the job of enforcing the FCC regulations for U.S. registered aircraft entering the United States to see if they had one while flying internationally. Under U.S. law the station license is still required for U.S. registered aircraft when entering the USA, although not for flying within the US.
In accordance with 47 CFR § 13.18, the Radiotelegraph (T), General Radiotelephone Operator (PG), GMDSS Operator (DO), GMDSS Maintainer (DM), Restricted GMDSS (RG) and Marine Radio Operator (MP) licenses convey the operating authority of the Restricted Radiotelephone Operator Permit (RR); if you hold one of these licenses, you would not need to apply for a separate Restricted Radiotelephone Operator Permit.
AOPA has been advocating for a U.S. – Canada reciprocal agreement that would exempt both U.S. and Canadian certificated pilots from requirements for restricted radio telephone operators permits and radio station licenses to operate in each other’s countries.