After the ressurection, just before Jesus ascends into heaven he gives all believers this final charge. "Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, teaching them to observe all that I have commanded you. And behold, I am with you always, to the end of the age." In Revelation 5:9 God is worshipped because he "ransomed people for God from every tribe and language and people and nation."
The heartbeat of God from the very beginning of creation has been for the nations. He seeks worshippers from all people groups of the earth. Missions exist because universal worship does not. While there are still people who are not actively worshipping God as their King we will go and support others to go.
We love people, and do not want to see anyone spend an eternity seperated from God. This however is not our primary motivation in taking to gospel to the ends of the earth. We go because God is worthy and deserves worship from every corner of his creation.