It's not whether it's more powerful. It's whether it's more appropriate for the Black players to rely on whitey to get their messages across, and I think the answer to that question is NO. They felt hurt because of racial prejudices and I think it would be natural for them to want someone who looks like them, who had their experiences, to be their face and voice.
The face and voice of the 1960s civil rights movement was King, not Johnson and not White people in power.