"When you take a census of the Children of Israel, each shall pay the Lord a ransom for his soul" (Exodus 30:12). Rabbi Levi Yitzchak of Berditchev reads this as God offering the Jewish people a strategy for surviving the attacks of the evil inclination, born from His overwhelming love for them.
God feels personally oppressed by the troubles of the Jewish people. This is not sentimentality. It follows from a fundamental principle: the continued existence of every creature depends on the radiance emanating from the Creator, who must restrain Himself behind various "veils" to prevent His brightness from fatally overwhelming His creatures. He provides sustenance to keep everything alive, as the verse states: "And You keep them all alive" (Nehemiah 9:6).
If this applies to all creatures, how much more so to God's chosen people. "For the Lord has chosen Jacob for Himself" (Psalms 135:4). The Jewish people are the means through which God illuminates the universe: "House of Jacob, let us walk by the light of the Lord" (Isaiah 2:5). When the Jewish people suffer, God Himself experiences the pain.
The sin of the golden calf had plunged the people into a spiritual crisis. The half-shekel contribution was not a tax. It was a symbolic ransom, a way of praying that Satan, the accusing angel who constantly seeks to seduce them into transgression, would be held at bay. The word tisa (תשא) in "when you take a census" also means "when you elevate." God was telling Moses: if you want to raise the status of the Jewish people from their depressed state, have each person pay a ransom for their soul.
Moses' role in saving Israel after the golden calf was not just intercession. It was elevation. He took a people who had fallen to the lowest point and showed them that even from there, a half-shekel of genuine repentance could ransom a soul from death.