Why do images of Jesus Christ look like they do?

The images of Jesus Christ that most Westerners are familiar with come from traditions that began in Europe with the Reformation and carried through the Renaissance. Fair haired, sleek, strangely androgynous. Fair enough. That style was all over the Western world for 500 years. But this is the 21st century. Jesus was clearly a Semitic Middle Easterner, unlikely to have blood relations that were Roman or Greek, the only realistically possible source of fair haired genes available at the time. It is likely he looked a little bit like Khalid Sheik Mohammed. So why not repaint or redraw Jesus Christ as he probably looked?