I've joined this thread late but my own view is that there is nothing wrong with people writing original songs and they don't necessarily have to be in traditional style as such.

However, before even contemplating embarking on regular song writing activites, the musician or singer should firstly have a good grounding in their own preferred area of music as opposed to those(many) who choose to purchase a guitar, ukele, or whatever and start plinking and wailing away.... the "should have stayed in the bedroom" types.

So, it ought to be a gradual process for a trad, folk, blues, jazz, even rock singer to progress into composing original as and when they are ready and the inspiration takes them. They should not think of "singer/song writing" as a genre in itself and just decide to write songs for the sake of it.

With a very few exceptions, all the respected songwriters have allowed themselves to have good musical grounding and gathered experience first..
eg Bob Dylan studied Woody Guthrie in particular, Ralph McTell... blues and old rag time, Dick Gaughan....traditional music etc, even The Beatles played rock and roll and other music for several years before they became prolific song writers. Their earlier albums included many covers.