Actually, in many countries the royal family was MORE important than in the medieval periods. Developed roads and such meant that communication was faster, and monarchs tended to live longer and, in some cases, have more control.
In Russia, for example, having the Tsar die would be a big freakin' deal. Even the English, with their constitutional monarchy, would've had a crisis on their hands if their king was captured/killed, since the monarch was an important nationalist symbol, much more so than in Medieval times when they were 'just' a leader.
However, they certainly had much less of a role on the battlefield, although MTW overexaggerated it as well. I'm pretty sure that no European monarch after 1750 or so took to the field. Peter the Great was probably the last one to do actual fighting himself.