I suggest adding a new color for the pseudo-class "myself".  Or adding an override for coloring that indicates "myself" and overrides that normal class colors.

When I'm tanking, I often use the color of the target-of-target frame as a quick sanity check that the mob I have targeted is hitting me and hasn't been pulled off by some other character.  Often I do this check as I'm tabbing or clicking through mobs in a large aoe pull, so I really am only glancing at the color of the target-of-target frame before doing some aggro move and going on to the next mob.  If the group contains a dps character of the same class, this quick glance may give a false positive because I see the other character who has the same class and thus the same color.

If it were possible to configure the target-of-target frame to display a special color on the health bar to indicate "myself" as opposed to my class color, it would make the sanity check more reliable.

I figure there's no reason to restrict this just to the target-of-target frame, though.  (Offhand, I can see target-of-focus being useful too.)