The more instruments you play, the better musically and as a writer you’ll be as you can see and understand the more intricate changes and progressions in chords and scales for those instruments. This means you can write multiple parts to the same song.
When I used to run a studio complex, we would have producers, engineers, bands/artists and tutors in and we’d talk. There seemed to be a pattern and agreed notion that if piano was the first instrument you learnt, learning others would come easier than if say guitar was your first instrument then learning other instruments.
Having piano as a first instrument seemed to help in engineering and production too. Any instrument helps and learning more instruments definitely helps in song writing and production.