I think what this boils down to is a continuum of translatability with nothing at either extreme.
Natsukashii may be more difficult to translate than Ohayo (ostensibly “Good morning”), but Ohayo has its own nuances that makes it not 100% translatable either.
For example, if you start working at 8 pm, you can greet your co-workers with Ohayo, but you couldn’t use Good morning. If you’re translating a novel and two characters greet each other with Ohayo at night, you may have to give some thought to capturing that nuance in English.
In the same way, if someone coos Natsukashii at a thrift store, finding the appropriate translation could take some work and depend on the situation. But it’s not untranslatable.
