Aside: pronunciations and other aspects of English have changed at a similar average rate in England as in Northern America. If settlers had retained their accent from the time of immigration, it may not be recognized as British English nowadays.

Accents of languages are not just geography and sociology, there are cultural and individual subtexts which must be treated with caution. Not easy to tell other persons what is "their own voice".

All other aspects of music follow different rules, much more tolerant of foreign influences. If we disapprove of such an influence, or find a particular artist not to be great enough, we speak of "mimicking", otherwise of "creative adaptation".