It seems safe to say that Jesus is proclaiming in John 8:24, that unless one believes that he is the only Savior who can take away one’s sins, the terrible prospect of paying for one’s own sins in eternal judgment awaits. This proclamation is true to the extent that whatever was said of Yahweh in the OT is directly applicable to Jesus Christ, God in the flesh. It also corresponds to what was already declared about Christ as far back as ch.1 in John’s gospel—that he is the Lamb of God who came to take away sins.
If that is not your primary view of the purpose of Christ, then you are no better off than the unbelievers in John 6-8 who want the Messiah for some other reason—whether that be earthly benefits or earthly power. It’s true that if anyone tries to engage with Christianity for some other reason, it is a completely worthless endeavor—”I want Christ to save me from my loneliness or my emotional instability or my financial pressure or my ongoing health issues or my relational tension with my spouse or family member.” Jesus actually came to die for our sinful responses to those things, and in doing so, he not only takes away the penalty of our sin, but also grants us power to no longer walk in darkness, but follow his light in spiritual life.