I think Songs are just Songs, and almost anyone could sing almost any Song, with their 'interpretation' bending it to 'fit' their general genre.
A 'good' Song should have that Adaptability, enabling a man or a woman to sing it, in a variety of genres.
If you haven't tried playing your Songs as a blues, do it right now.
Get a jaunty Rhythm going and play it as country.
Rock it and see if you can make it work.
I think lots of Songs CAN work in those variations. Try yours and see. Slow them down. Speed them up.
Varying the Prosody of how the Lyrical vocalization and Melody 'marries' to the tempo, the beat, can be very educational.
And that flexibility of how a Song 'can' be executed widens the potential for who could fit it logically into their repertoire.

There will always be another song to be written. Someone will write it. Why not you? www.garyeandrews.com