What used to be the norm was that there were songwriters who wrote songs and singers who performed them. Neither was expected to be good at the other's craft. How many songs did Frank Sinatra write?

A few were good at both, and made their names singing their own songs. There are obvious financial advantages from this, as well as having a unique and personal repertoire. Somewhere along the way the idea took hold that this was somehow better than singing someone else's songs, and the singer-songwriter became venerated. This in turn has led to the idea that a singer ought to write their own songs, and as a result we have some dreadful rubbish inflicted on us.

What is important is to have a good song well performed. It shouldn't matter if the person who wrote it is not the person who performs it.

The issue of people imitating other musicians' performances is entirely different. The answer is not to write one's own songs but to apply more thought to one's own interpretation. However the fact is that many audiences prefer a familiar version, or something close to it, than an individual interpretation.