No, it isn't God's mission to make everyone great. Not everyone can be great like Joseph who God gifted and prepared to run an entire country.
Being a Christian isn't about being great as the world defines greatness. It's about serving God in the way God calls you to serve Him using the gifts God has given you. You might be called to read to terminally ill children. Or to show hospitality to new people in your church. Or to clean at the church.
Well, we all have different beliefs about God. To me God is like a paternal father, a parent. No parent would ever want anything less for his children. And so I know that God wants to tap these gifts to be able to serve like what you said. God bless!