One theory regarding God's "miracles" (supernatural acts) is to prove both his existence and the fact that he is supernatural and thus the Creator. In that respect, Jesus's supernatural miracles confirm God's existence, and that Jesus speaks for God. But the prophets did the same thing.
But less clear in your article is why did God feel compelled to come to earth in the body of a human rather than send prophets as he had done previously and empower them to perform miracles as He had done before.
In other words, your explanation is not wrong, it just falls terribly short. Jesus's coming to earth was part of a much bigger plan which included His death on a cross and not just His teachings.
Beginning with Cain and Abel and highlighted in the story of Abraham, the idea of sacrifices to God as the means to atone for sins against God and accept responsibility and punishment for our sinful acts is clear. Think of sacrifices as "loss", when someone sacrifices, they give up something of value when such sacrifices are made for the forgiveness of sins, it serves as a means to compensate the "injured party" (in this case, God). Yet God is clear, the actual sacrifices mean nothing to Him, it is the motivation to reconcile that He values and the acceptance by us that we have wronged God.
So, sin is an issue and deserving of punishment. But just as we take hope in Jesus's death that God loves us so much that He accepts Jesus's death as our "sacrifice". We should also "sacrifice" through our acceptance of the loss dealt to us by those who sin against us. In that sense, your focus on love is correct, but "love" does not detract from the issue of sin... it serves as a means to resolve it.