Well, I prefer to use the term "interpretation" as opposed to cover.

Surely, people don't write songs or tunes with the express wish that no one should sing or record them other than themselves. Of course, they may have their own views on how these are interpreted by others and not always enjoy the result but that's a different matter.

If nobody else sang or played the songs and tunes, then they would die out along with the composer.

As for creating exact copies of a composer's work in terms of musical arrangements etc, etc, this, of course, is something which should be avoided. Everyone should interpret music and song in their own way.

However, until an artist develops their own style and and are learning their craft, they will inevitably be influenced by other musicians and singers. For instance, you can't become a traditional fiddler without checking out and practising at least some of the existing playing styles.
Of course, you may never need to study Donegal music, for instance, or old time American music to become a traditional fiddler especially if you are concentrating on Scottish music but the wider the influences are the better. You don't have to try to emulate all players or singers, of course, but nobody can learn to become experienced players and singers while living within a musical vacuum.