One of the hottest rock/pop songwriters today is Billy Steinberg, who co-wrote with Tom Kelly "Eternal Flame" (for The Bangles), ""So Emotional" (for Whitney Houston), "True Colors" (for Cyndi Lauper) and "Alone" (for Heart) among others. Steinberg advised in an interview for the May/June issue of American Songwriter, that he doesn't aim for a particular artist when making a demo. "If you demo it for a particular artist and they don't take it, then it sounds too much in their direction. We demo the song for the song's sake."
I've heard the question asked at several Nashville songwriting seminars and Louisville workshops, and the answer by successful songwriters is overwhelmingly similar to Steinberg's.
Paul Overstreet, a "not so shabby" singer and also a very hot country songwriter who wrote "Same Ole Me" (for George Jones), co-wrote "On the Other Hand" (with Don Schlitz) and "A Long Line Of Love" with Thom Schuyler, among other hits, made a similar statement in last year's July/August issue of American Songwriter. He said, "I think the song has to say what it is trying to say and then if it fits an artist, if they feel like they can say what the songs says, then at that point you have a relationship. But if you sit down to write a song for the artist, then the artist is the center of attention and the song is just a sugar coating."
I agree with Overstreet and Steinberg that the real focus is on the song itself. After all, nobody is going to do the song if it's not good enough. Hopefully, when and if that happens you won't have much trouble pitching a song of the quality of "On the Other Hand" to several country artists/publishers or a song such as "Eternal Flame" to several rock/pop artists/publishers without being slanted toward anyone in particular. The lyrics, melody and basic elements of a well-written song are what's important and each one of these great songs have them.