In some ways I agree with Michael P, and in others I don't. There are some audiences who want to see, let's say, the Beatles, but obviously can't. So they like to see the best Beatles Tribute bands, who typically try to be as much a 'photocopy' of the originals as they can, since that is specifically what the audience wants. And some of them are extremely good at it, which requires a lot of skills, including musicianship and acting ability, and also a certain amount of luck, such as looking vaguely like the person concerned.

Then there are those musicians who are forced into it, as it were. Taking an example from a completely different field, there is an Indian restaurant near here who tried for several years to sell authentic meals in the style of the various districts. No luck: all the diners wanted, really, was generic stuff exactly as you could get in 90% of the other Indian restaurants in the country, so in the end they had to admit defeat and go for "the standard menu". That happens a lot with musicians as well: getting gigs playing known and standard material is a lot easier than with your own stuff (Since I raised it, all the early Beatles material is like that.)

Then there is the fact, as someone alluded to above, that a lot of self-written material is simply not very good, or (less judgementally) is not something that transfers well from the composer to others. A frequent cause of this is when the song is about some personal experience that the composer had. Since others didn't have that experience it can be difficult for others to sing it well. It is, in my humble opinion, part of the reason most traditional songs are in the third person, whereas most pop music is first person.

So those are some of the reasons why I partially agree with Michael. On the other hand, I much prefer to hear/sing traditional music (whatever that means), or a new song "that speaks to me", rather than a cover.