It’s interesting how praying for others reveals so much of your own heart. As you pray, you are often caused to dwell on your interactions with these people, interactions which so often fall short.
I encourage you to try it! Pray for one person you interact with frequently and see how God stirs up in You a desire to change so you can be more effective for Him in that relationship.
Maybe that’s a small reason why we pray for others– it’s Gospel strategy as we’re forced to ask God to transform our own hearts to love the other person and share Christ with them better.