This is a good approach, but we run the risk of becoming just like those Jesus did battle with in the Gospels--the Pharisees and teachers of the law. This approach by itself will not turn us into Pharisees, but it can contribute to a Pharasaical attitude by privileging doctrinal points above the relational connection we have in Christ.
The Gospels and the Letters should be read together. Jesus teaches us much about our inner lives, where our heart's desire should be, and how we can be truly pleasing to God. Paul does the same in his letters, but it's easier to overlook there because he also teaches about how churches should operate.
We need balance. Gospels only leave us without any real sense (except a constructed sense) of how the early church functioned. Letters only leave us without any real knowledge of the founder of our faith. We need both, in tandem with each other.
Not Gospels vs. Letters, but Gospels + Letters = The Whole.