maybe it could be a good practice for developing of songwriting skills to learn some minimal basics of playing another different-kind instruments...or at least LISTEN a lot of instruments. I remember my first experience of playing classic music (Vivaldi, Bach etc). Although the notes were played right, I was totally clueless about what original instruments this music was written for. My teacher explained to me a huge difference between bow-made sound (like sound of cello, violin) and finger-made one (guitar, bass guitar). Then I watched lots of video where cellists played classics and it totally changed my level of understanding and playing music. I became to imitate their sound, sustain, articulations, rubato-tricks etc. I had not even touch cello, but my playing became much better!
The same story about jazz. Listening for great saxophone-, trumpet-players contributes colossal value into your mind and helps you to perform that music in correct way. These people have a natural necessity to make pauses while playing to breath in, so their phrasing is closely related with human speech.
Bottom line: even listening for multiple instruments will greatly develop both your playing and songwriting.:)