Good points, Rahere.
And, as Don said, it depends on the song.
I've written quite a few songs, at least half of which I do not perform live, because I composed them with harmony (or other vocal backup) parts in mind, I overdubbed my own voice on the recordings, and the songs just do not sound the way they're supposed to when done as solos, no matter how good the voice. Some of my others either really don't need harmony or a canticle or counterpoint, etc., and possibly may sound better as solos. (I'd say all of them, though, can benefit from more than one instrumental backup or break.)