The Benefits
Perhaps the most important thing that playing an instrument can bestow upon a songwriter is respect. Publishers, producers, A&R reps, recording artists, and other songwriters will be more likely to respect you and your songs if they know you can play. Of course, there's someone even more important than those people: You, the songwriter, will have more confidence and self-respect if you know that you can write and play a song all by your self without any help from anyone.
If you're already a professional musician, you may be able to use your skills to help advance your songwriting career. Many professional songwriters have made business connections by playing live and/or recording for other people. There is nothing more valuable to you, business-wise, than a direct connection to an artist or producer.
And that's not all. If you play an instrument, you won't have to rely on others to figure out the chord progressions to your songs. You won't have to hire a musician to play for you at an open mike or writer's night, and you'll be able to communicate musical ideas more clearly and more quickly to other musicians in both live and studio settings. This gives you power and independence.
It also means that you won't have to get that embarrassed, apologetic look on your face when someone asks you to play something you wrote. When it comes to proving that you're a songwriter, playing one of your songs is much more convincing than pointing to a notebook or waving a CD.
Brainstorming with an InstrumentWhen it comes to the actual writing of a song, playing an instrument can open up a whole range of options. Doodling around on an instrument is one of the most popular methods used by successful songwriters for coming up with new ideas.
Sometimes just learning a new chord or experimenting with a different groove or time signature can be all it takes to start you writing a hit song. Playing an instrument can also make for better communication and a more balanced workload when you co-write with another player.

