When Britain’s Prince Harry and American actress Meghan Marklewalked down the aisle May 19, royal-wedding fans watched on television around the world.

On the TV screen to enlighten many of them was a commentator named Thomas J. Mace-Archer-Mills, Esq. He has built a media persona over recent years as one of Britain’s authorities on the royalty, and he appeared in dozens of interviews leading up to the wedding to explain and defend the monarchy.

In...