Paul covered the Gospel quite well,and oh yeah,those 4 Gospel dudes did too,so I think it is covered quite well without ole' James having to cover it,if God wanted him to cover other things.The fact that James is in the Bible,would point to the fact that he believes the Gospel,and covers in more areas how to be pleasing to God,for the Gospel means nothing in your life,if you are not pleasing to God in how you behave,and lifestyle.
All scripture is given by inspiration of God,and James focused on what God wanted him to focus on,which James kind of reminds me of the book of Proverbs,for he still preaches the Gospel in his own way,and going more in to different areas of how to be pleasing to God than Paul did.
God had Paul focus on what he was supposed to,preaching the Gospel like a big dog,and telling us about it,and had James focus on what he was supposed to,going to more different areas of how we should behave to be pleasing to God,and he still said he was a servant of God,and the Lord Jesus Christ.
Like the disciples all displayed Jesus in a different way.
Matthew: Christ is the Son of David, rightful heir to the Messianic throne. Here we see Christ's royal genealogy, the visit by the magi from the East to announce His kingly birth, and the proclamation of His laws in the Sermon on the Mount.
Mark: Here we find Jesus as the Servant of God. Although Jesus came as God to earth, He completely submitted Himself to the will of the Father in heaven and took on the form of a servant. Anything extraneous to that theme is excluded, which is why the narrative contains no references to Jesus's birth or youth.
Luke: To Luke, Jesus is the Son of Man—fully human but unlike any other human being in His perfect submission to God's will. For this reason, Luke traces the genealogy back to Adam (the first human).
John: John presents Jesus as the Son of God—fully divine. Jesus is not only flesh and bones, but He is also the Creator of all things in the beginning. Jesus reveals His nature as "I am," a title God gave as His own.
All scripture is given by inspiration of God,and if God does not have someone cover something,someone else will surely cover it,and God will have them write whatever He will have them write.