We should not view “the world” in John 3:16 as just the elect because there is a strong emphasis in the Scriptures on the love that God has for the world that has turned against Him.
In John’s gospel, “world” usually means either “not just the Jews” or “the world as a fallen entity.” In the context of John 3:16, both of these things are true. The wonder of the gospel is that God so loved this fallen world that He gave His only Son. There is also an aspect of “the world” that points to God’s love not being exclusively for the Jews. So, to limit that statement to the elect would diminish the fact that it is the lost world that has drawn the compassion of God.