My understanding is that Harry and Meghan's son has not actually even really been denied the title Prince. He doesn't as yet actually qualify for the title. It is something granted to sons and grandsons of monarchs with that only stretching another generation for the sons of the person directly in line for the throne. So the only one of the new generation that actually qualifies automatically as a Prince at the moment is George who is the son of William who will be heir to the throne once his father becomes king. Harry's children would only actually qualify as Prince or Princess when the Queen dies and Charles takes the throne. The Queen gave the title by special dispensation to the other children of William and Kate I take it because William is directly in line to the throne. They are the kids of someone who is destined to be, and is being groomed as, a future king. Whether folks in America like it or not. William and Kate have the nuclear family that will one day sit around the throne. Not Harry and Meghan who are the also rans of the family like Anne and Edward were - and Margaret before that. I find it hard to have sympathy for the idea that one incredibly spoiled family unit thought themselves slightly less spoiled in the way of receiving titles than the older sibling and his family.