Writing your own songs is not a life or death issue for your worship team.
You don’t need it to be successful. It’s quite OK to sing the great songs of worship leaders like Matt Redman, Paul Baloche, Tim Hughes, Israel Houghton, Kari Jobe, and others.
The presence of God can still be present in your gatherings and the favor of God can still fill your ministry.
But I think you should give songwriting a try. And, I think you should consider hosting a songwriting retreat with some members of your worship team.