So while what you say may be true, and it's certainly true as an application of 'presentism' to an object from antiquity. We certainly are inclined to see that from our contemporary positions.
Then again, it is fair to remember that it was Byzantines during the rule of Justinian who created the oldest images of white Jesus not Anglo-Saxon colonials wanting slaves.
We know from archeology that it was common for Hellenic and Roman people to represent their dieties in terms of the appearence of the mortals who worshipped them (although the scripture reverses that to God creating the chosen people in His image).
This direct correspondence of worshipers' appearance and that of their deities is likely a matter of a sociological phenomenon termed homophily (from phily for like or love, and homo for same) a term used to discuss a pattern of social assortment in humans. In that process people are suggested to divide into coherent groups that have internal similarites, not necessarily based on nationality or heritable pigmentation, but also by income/power, intelligence/education, political views, religious views, sexual preferences etc.
I can't argue against the possibility that the Byzantines (who are most responsible for creating Christianity and the path of our imaginations of Jesus) created a white Jesus for reasons such as recruitment into the church and an 'otherization' of colored people. But, it's also possible that while Roman and Hellenic Byzantines were diverse, the educated elite were still mostly white and they simply applied the appearance of the majority to their imagination of the emerging new deity.
There really are quite interesting things hiding in the study of historical iconography. One of them is the timing of the emergence of a white Jesus (who according to the writings wasn't Causcasian per se--not from the Caucus-- but a Semite). The earliest existing icons aren't really very early, and they are definitely Byzantine and not from Israel, there is no reason to believe they are accurate representations.
In the iconography academics have found meaningful patterns, but that have less to do with his whiteness.
Most of the icons divide the Jesus images into left and right halves. His right side (left as we view the icons) is typically thought to represent his Divinity, also indicated by his right hand, often posed to suggest he is giving a blessing. The left side (on the viewers right) is considered his humanity, as indicated by his left arm tightly clutching a codex of the Gospels representing the authority of The Word and The Church that controlled that word.
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