But some countries may refuse that (for example, it seems like Belgium has imposed US Certificates to fly N-Reg airplanes in Belgium).
Do you have a reference for that, Orbifly?
I don't doubt you - I am genuinely interested.
As far as I can see, Belgium might be able to do that only for its own citizens, without breaching ICAO.
One hears these things around the place. Obviously they won't be in the national AIP; they will be buried deep in the local aviation law.
Other examples: Irish CAA banning FAA license holders flying under the privileges of the FAA Class 3 medical. Denmark banning N-reg from being parked there. Spain banning its own citizens from exercising the privileges of any non-JAA license in Spanish airspace. Etc.